Question

You are told that the volume of a sphere is given by V = πd³/4, where V is the volume and d is the diameter of the sphere. Is this equation dimensionally correct?

Answer 1

Answer:

The given equation is not correct.

Step-by-step explanation:

It is given that the volume of a sphere is

$V=\frac{\pi d^3}{4}$              .... (1)

where V is the volume and d is the diameter of the sphere.

We need to check whether the equation is dimensionally correct.

We know that the volume of a sphere is

$V_1=\frac{4}{3}\pi r^3$                   ... (2)

where, r is radius.

Diameter of sphere is twice of its radius, i.e., d=2r.

Substitute $r=\frac{d}{2}$ in equation (2).

$V_1=\frac{4}{3}\pi (\frac{d}{2})^3$

$V_1=\frac{4}{3}\pi (\frac{d^3}{2^3})$

$V_1=\frac{4}{3}\pi (\frac{d^3}{8})$

$V_1=\frac{1}{6}\pi d^3$

$V_1\neq V$

Therefore the given equation is not correct.