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.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.