Q.Each side of a cube is measured to be 7.203m .What are the total surface area and the volume of the cube to appropriate significant figures?

Check the correctness of agiven physical relationship?

v=/pr4 / 8nl

where v=volume of the fluid flowing through the tube per second

p=pressure difference across the ends of the tube.

r=radius of the tube.

l=length of the tube.

n=co-efficient of viscosity.

**(a)**

surface area of a cube, A = 6.x^{2}

volume of cube, V = x^{3}

so, here

x = 7.203 m

thus, we have

A = 6x(7.203)^{2}

or

A = 311.299 m^{2}

and

V = 373.714 m3

(b)

here the dimensions of the different physical quantities are

for volume flow rate we have

[v] = [M^{0}L^{3}T^{-1}]

the rest are

[P] = [M^{1}L^{-1}T^{-2}]

[r] = [M^{0}L^{1}T^{0}]

[l] = [M^{0}L^{1}T^{0}]

[n] = [M^{1}L^{-1}T^{-1}]

so,

v = Pr^{4} / 8nl = [M^{1}L^{-1}T^{-2}].[M^{0}L^{1}T^{0}]^{4} **/** [M^{1}L^{-1}T^{-1}].[M^{0}L^{1}T^{0}]

or

v = [M^{1}L^{3}T^{-2}] / [M^{1}L^{0}T^{-1}]

so, according to the formula the dimensions of the volume flow rate are

**v = [M**^{0}**L**^{3}**T**^{-1}**]**

which is equal to its real dimensions. So, the formula is real.

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