A cone of maximum size is carved out from a cube of edge 14cm FInd out the surface - Maths - Surface Areas and Volumes

Question

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

Lalit Mehra · Accepted Answer

Dear Student!

The base of the largest right circular cone will be the circle inscribed in a face of the cube and its height will be equal to an edge of the cube.

Given, Edge of the cube = 14 cm

Radius of base of the cone, r $= \frac{14 cm}{2}$ = 7 cm

Height of the cone, h = 14 cm

Slant height of the cone, $l = \sqrt{r^{2} + h^{2}}$

$∴ l = \sqrt{(7 {cm)}^{2} + (14 {cm)}^{2}} = \sqrt{49 {cm}^{2} +196 {cm}^{2}} = \sqrt{245 {cm}^{2}} = 7 \sqrt{5} cm$

Surface area of the cone curved out of the cube

$= π r (r + l) = \frac{22}{7} \times 7 cm × (7 cm + 7 \sqrt{5} cm) = 154 (\sqrt{5} + 1) {cm}^{2}$

Curved surface area of the cone carved out of the cube

$= π r l = \frac{22}{7} \times 7 cm × 7 \sqrt{5} cm = 154 \sqrt{5} {cm}^{2}$

Surface area of the remaining solid

= 5 × (edge of the cube)² + Curved surface area of cone

= 5 × (14 cm)² + $154 \sqrt{5}$ cm²

$= (980 + 154 \sqrt{5}) {cm}^{2}$

Thus, the surface area of the remaining solid is $(980 + 154 \sqrt{5}) {cm}^{2}$ .

Cheers!

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 ....