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Syllabus

a cone of radius 10 cm is divided into two parts by drawing a plane through the midpoint of its axis , parallel to its base . compare the volume of the two parts

a farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field , which is 10m in diameter and 2 m deep. If water flows through the pipe at the rate of 3km/hr , in how much time the tank be filled ?

A well of diameter 3m ,dug 14m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4m to form an embankment. Find the height of the embankment.

The height of a cone is 30cm.A small cone is cut off at the top by a plane parallel to the base.If its volume be 1/27 of the volume of the given cone,then what is the height above the base at which the section is made?

Example 2:A right triangle, whose perpendicular sides are 30 cm and 40 cm, is made to revolve about its hypotenuse. Find the surface area of the double cone so obtained.can any 1 explain me with video..so it will be more clear..

water is flowing at the rate of 15km/hr through a pipe of diameter 14 cm into a rectangular tank which is 50m long and 44m wide . find the time in which the level of water in the tank will rise by 21 cm

In triangle ABC, AB = 20, AC=15, BC=7Line segment BC is extended past C to D so that triangles DAB and DCA are similar. Find DC.

A hollow cone is cut by a plane parallel to the base and the upper portion is removed. If the curved surface area of the remainder is 8/9th of the curved surface of the whole cone, find the ratio of the line segments into which the cone's altitude is divided by the plane.

An overhead tank has been constructed to supply water to a village with a population of 3140 at the rate of 25litres per head per day.. water is pumped into it through a pipe of diameter 10cm, the rate of flow being 4m per sec. how long will it take to fill the tank every morning.. pie= 3.14

a cylinder , a cone and a hemisphere of equal base have the same height. what is their ratio in their volumes ?

A hemispherical tank , full of water , is emptied by a pipe at the rate of 25/7 litres per second. How much time will it take to empty half the tank if the diameter of the base of the tank is 3 m ?

spherical marbles of diameter 1.4cm each are dropped into a cylindrical beaker of radius 3 cm containing some water. find the no. of marbles that should be dropped into the beaker so that water level rises by 5.6 cm

A cone of maximum size is carved out from a cube of edge 14cm . FInd out the surface area of the cone and of the remaining solid left out after the carved out . Plzz Answer ....

Please don't provide a link to a similar question, as I know the method, and I just wanted to check my answer.

Thank You.

A right triangle whose sides are 15 cm and 20 cm is made to revolve about its hypoteneous.Find the volume and the surface area of the double cone so formed. (Take pie = 3.14

A well of diameter 7m is dug 22.5m deep. The earth taken out is spread evenly all around it to a width of 10.5 m to form an embarkment.Find the height of the embarkment.

the rainwater from a roof 22m*20m drains into a cylindrical vessel having diameter of base 2 m and height 3.5m . if the vessel is just full , find the rainfall in cm.

pls do this problem in simple method

Also, how to convert cm cube to litres??????

total surface area of an hollow sphere and hemisphere?

8. Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm?

9. A solid iron cuboidal block of dimensions 4.4 m × 2.6 m × 1m is recast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe. 10. 500 persons are taking a dip into a cuboidal pond which is 80 m long and 50 m broad. What is the rise of water level in the pond, if the average displacement of the water by a person is 0.04m3 ?

11. 16 glass spheres each of radius 2 cm are packed into a cuboidal box of internal dimensions 16 cm × 8 cm × 8 cm and then the box is filled with water. Find the volume of water filled in the box.

12. A milk container of height 16 cm is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of Rs. 22 per litre which the container can hold.

13. A cylindrical bucket of height 32 cm and base radius 18 cm is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.

14. A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diameter and height of the cylinder are 6 cm and 12 cm, respectively. If the the slant height of the conical portion is 5 cm, find the total surface area and volume of the rocket [Use π = 3.14].

15. A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains 19 41 21 m3 of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building?

16. A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius 1.5 cm and height 4 cm. How many bottles are needed to empty the bowl?

17. A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is equal to the radius of the cone.

If the diameter of a sphere is decreased by 25%, then by what percent its curved area would decrease?

A sphere and a cube have the same surface area. Show that the ratio of the volume of

the sphere to that of cube is √6: √p .

the barrel fountain pen cylindrical in shape is 7cm long and 5mm in diameter. a full barrel of ink in the pen is used up in writing 330 words

on an average.

how many words would use up a bottle of ink containing one fifth of a litre?

A rectangular container,whose base is square of side 5cm stands on a horizontal table and holds water upto 1 cm from the top.When a cube is placed in the water it is completely submerged.The water rises to the top and 2 cubic cm of water overflows.Calculate the volume of the cube and also length of its edge.

A sphere of diameter 12 cm is dropped in a right circular cylinder vessel partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by 32/9cm. find the diameter of the cylindrical vessel.

a plot of land is in the form of a rectangle has dimensiond 240cm X 180cm. a drainlet 10m wide is dug all around and the earth dug out is evenly spread over the plot increasing its surface level by 25cm. find the depth of the drainlet.

a copper wire 3mm in diameter ,is wound about a cylinder whose length is 12cm , and diameter 10cm so as to cover the csa of the cylinder . find the length and mass of the wire , assuming the density of copper to be 8.88g per cm3

A solid metallic sphere of radius 3 cm, is melted and recast into small solid spherical balls of radius 0.3 cm. find the number of balls formed

a bucket made up of metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. find the cost of the bucket if the cost of the metal sheet is Rs. 15 per 100 cm

^{3 }( use pi= 22/7)if h,c,v are respectively the height, curved surface area and the volume of a cone.prove that

3 pie v h cube - c2h2 + 9v2 =0

the radii of the ends of the frustumof a cone 45cm high are 28cm and 7 cm. find its volume , the C.S.A & the T.S.A.

A hemispherical depression is cut-out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

What is the CSA, TSA and volume of a frustum?

The difference between the outer and inner curved surface areas of a hollow right circular cylinder, 14cm long, is 88cm2. If the volune of metal used in making the cylinder is 176cm3, find the outer and inner diameters of the cylinder

If -2 is a root of the quadratic equation x2 -px -5 =0 and the quadratic equation x2 +px +k =0 has equal roots ,find the value of k.

a sphere of diameter 6cm is dropped in a right circular cylindrical vessel partly filled with water . the diameter of the cylindrical vessel is 12cm. if sphere is completely submerged in water by how much will the level of water rise?

the interior of building is in the form of a right circular cylinder of radius 7cm & the height 6m surmounted by a right circular cone of same radius & of vertical ngle 60

^{0}find the cost of painting the building from inside at the rate rs 30/m^{2}A conical vessel of radius 6cm and height 8cm is completely filled with water. A spere is lowered into the water and its size is such that when it touches the sides, it is just immersed. What fraction of water overflows?

a bucket i sin the form of frustum with the capacity of 12308.8 cm cube.the radii of the top and bottom of circular ends are 12 cm and 20 cm resp.find the hieght of the bucket and also the area of metal sheets used in making the bucket.(use pie=3.14)

What is the difference between curved surface area & total surface area?

Two cubes each of side 4cm are joined end to end.Find the surface area of the resulting cuboid

A shuttle cock used for playing badminton has the shape of a frustum of a cone mounted on a hemisphere (see figure). The diameters of the ends of the frustum are 5 cm and 2 cm , the height of the entire shuttle cock is 7 cm. Find the external surface area. (Take Pie=22/7) .

A well of diameter 3m, is dug 14m deep The earth taken out of it has been evenly spread all around it to a width of 4m, to form an embankment Find the height of the embankment use pi=22/7

The volume of a solid metallic sphere is 616cm

^{3}. It is melted and recast into a cone of height 28cm. Find the diameter of the base of the cone so formed?If the diameter of the cross section of the wire is decreased by 5%,how much %will the length be increased so that the volume remains the same

A right triangle has sides 15cm and 20cm forming the right angle is rotated about the hypotenuese.find the volume of the double cone formed.

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Find the ratio of their volumes>

From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm

^{2}.Given that,

Height (

h) of the conical part = Height (h) of the cylindrical part = 2.4 cmDiameter of the cylindrical part = 1.4 cm

Therefore, radius (

r) of the cylindrical part = 0.7 cmTotal surface area of the remaining solid will be

= CSA of cylindrical part + CSA of conical part + Area of cylindrical base

The total surface area of the remaining solid to the nearest cm

^{2}is 18 cm^{2}.Why C.S.A. of cone is added instead of subtracting(cause we have to find T.S.A. of remaining part)???

plz explain

For calculating total surface area of a bird bath in the shape of a cylinder with a hemispherical depression at one end , y dont we take the area of the base of the area. As in the book it is shown only CSA of Cylinder and CSA of hemisphere... kindly explain as for total surface the area of base has also to be taken into account

The interior of a building is in the form of a cylinder of diameter 4.3m and height 3.8m, surmounted by a cone whose vertical angle is a right angle. Find the area of the surface and volume of the building.

do we always have to use the double cone method whenever the question specifies that a side of a right circular cone is revolved about a side?? please i need the answer urgently..

The volume of cube is 8a

^{3 }. Find its surface areaThe height of right circular cone is trisected by two plane parallel to its base. Show that the volume of the three propotion from top are in ratio 1:7:19.

(i am repostingthe question plsansurgent):a metal cube of side 11 cm is completely submerged in a water contained in a cylindrical vessel with diameter 28 cm, find the rise in level of water ?A swimming pool is filled by 3 pipes with uniform flow, The first two pipes operating simultaneously, fill the pool in the same time during which the pool is filled by the 3

^{rd}pipe alone. The 2^{nd}pipe fills the pool 5 hours faster than the 1^{st}pipe & 4 hours slower than the 3^{rd}pipe. Find the time required by each pipe to fill the pool separately.An ice-cream seller has two types of ice-cream containers one in the form of a cylindrical shape and another in the shape of a frustum. Both have the same height 7cm and the diameter of cylindrical container is 7cm. Upper and lower radii of frustum are 3.5cm and 3cm respectively.

(i) Calculate the volume of both the containers

(ii) If the cost of the containers is te same and the seller prefers to sell ice-cream in the cylindrical container, then which value is depicted by the seller

Do not link another topic.cost of painting the total outside surface of a closed cylindrical oil tank at 60 paise per sq. dm is rs.237.60 . the heigth of the tank is 6 times the radius of the base of tank . find its volume correct to two decimal point...? and is que. in easy

what is meant by surface area

is it tsa or csa??????

A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm (see the given figure).

t can be observed that

Radius (

r) of cylindrical part = Radius (r) of hemispherical part =Length of each hemispherical part = Radius of hemispherical part = 1.4 cm

Length (

h) of cylindrical part = 5 − 2 × Length of hemispherical part= 5 − 2 × 1.4 = 2.2 cm

Volume of one gulab jamun = Vol. of cylindrical part + 2 × Vol. of hemispherical part

Volume of 45 gulab jamuns == 1,127.25 cm

^{3}Volume of sugar syrup = 30% of volume

plz tell me why it is voulume of gulab jamun is taken to find the sugar suyrup. why we can't take area of gulab jamun in the place volume because container contain gulab jamun we can take their area and then the volume of container. im not able to understand the question. please try to explain with proper diagram.

why are we subtracting in the base area as we know that CSA of hemisphere actually means the area of hemisphere without base

Already the base is excluded as we are adding only CSA of hemisphere then again y minus base area

I don't need answer just y need to add base area

Water is flowing at the rate of 3km/hr through a circular pipe of 20cm internal diameter into a circular cistern of diameter 10m and depth 2m.In how much time will the cistern be filled? Also, plzz tell that here what is meant by cistern?????

A cylindrical copper rod of diameter 1 cm and length 8 cm is drawn into a cylindrical wire of length 18 m and of unifiorm thickness. Find the thickness of the wire.

A bucket, made up with metal sheet is in the form of frustrum of a cone of height 24 cm with diameter of the two end as 30 cm and 10 cm repectively. find the cost of the metal sheet used if it cost is Rs. 10 per 100 cm square.

A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs 500 per m

^{2}. (Note that the base of the tent will not be covered with canvas.)A tent consists of a frustum of a cone, surmounted by a cone. If the diameters of the upper and lower circular ends of the frustum be 14m and 26m respectively , the height of the frustum be 8m and the slant height of the surmounted conical portion be 12 m, find the area of canvas required to make tent . (Assume that the radii of the upper circular end of the frustum and the base of surmounted conical portion are equal).

just give me answer ....no need to show all the steps...

find the area of the shaded region where ABCD is a square of side 14cm . ( four equal circle inside the square) . And please explain me how the radius is obtained .

water running in a cylindrical pipe of inner diameter 7 cm, is collected in a container at the rate of 192.5 litres per minute.find the rate of flow of water in the pipe in km/hr

the derivatio of the formula of frustum of cone

A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the milk which can completely fill the container, at the rate of Rs.20 per litre. Also find the cost of metal sheet used to make the container, if it costs Rs.8 per 100 cm

^{2}. [Take π = 3.14]in one fortnight of a given month ,there was a rainfall of 10cm in a river valley .if the area of the valley is 97280 km sq. ,show that the total rainfall was approx. equivalent to the addition to the normal water of the three rivers each ,1072 km long ,75m wide and 3m deep.

PLEASE HELP THIS ANSWER IS NOT AVAILABLE ON MERITNATION NCERT SOLUTION.

How to derive the formula for voulume of frustum of a cone?

- How to derive the relation bnetween the orginal cone radius / height to the portion of the cone that is removed?

Water is flowing through a cylindrical pipe, of internal diameter 2cm, into a cylindrical tank of base radius 40cm, at the rate of 0.4m/s. Determine the rise in level of water in the tank in half an hour.

Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7cm containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6cm??(please explain step-wise) :))A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream

I cant understand any example!!!! Please upload videos for them! Thumbs up if you want videos explaining these examples!!!!!!!! Please add vids.

Thanks

A solid toy is in the form of a hemisphere surmounted by a right circular cone.Height of the cone is 2cm and the diameter is 4cm. If a right circular cylinder circumscribes the solid,find how much more space it will cover.

can you tell the easiest way to remember the formulas of all solids?