# 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  /  8nlwhere v=volume of the fluid flowing through the tube per secondp=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.x2

volume of cube, V = x3

so, here

x = 7.203 m

thus, we have

A = 6x(7.203)2

or

A = 311.299 m2

and

V = 373.714 m3

(b)

here the dimensions of the different physical quantities are

for volume flow rate we have

[v] = [M0L3T-1]

the rest are

[P] = [M1L-1T-2]

[r] = [M0L1T0]

[l] = [M0L1T0]

[n] = [M1L-1T-1]

so,

v =  Pr4 / 8nl =  [M1L-1T-2].[M0L1T0]4 / [M1L-1T-1].[M0L1T0]

or

v = [M1L3T-2] / [M1L0T-1]

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

v = [M0L3T-1]

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

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