Question

The volume of a sphere of diameter d is:
A. $\dfrac{{\pi {d^3}}}{3}$
B. $\dfrac{{\pi {d^3}}}{6}$
C. $\dfrac{{2\pi {d^3}}}{3}$
D. $\dfrac{{\pi {d^3}}}{4}$

Answer 1

Hint: We know that the volume of a sphere with radius r is given by $\dfrac{4}{3}\pi {r^3}$, also we know that diameter d is given by \[d = 2r\], so using this two equations we will find the volume of the sphere in terms of diameter.

Complete step by step Answer:

We know that the volume of a sphere with radius r is given by $\dfrac{4}{3}\pi {r^3}$
Given that the diameter of the sphere is d. Therefore radius is $\dfrac{d}{2}$.
Therefore, The volume of the sphere is
\[ = \dfrac{4}{3}\pi {\left( {\dfrac{d}{2}} \right)^3}\]
On simplification we get,
\[ = \dfrac{{\pi {d^3}}}{6}\]
Therefore volume of a sphere of diameter d is \[\dfrac{{\pi {d^3}}}{6}\].
Hence (B) is the correct option.

Note: Note the formulae of finding the volume of the following figures.

Figure	Volume
Cube	\[{a^3}\]
Cuboid	\[\begin{array}{*{20}{l}} {{\mathbf{l}} \times {\mathbf{b}} \times {\mathbf{h}}} \end{array}\]
Sphere	$\dfrac{4}{3}\pi {r^3}$
Hemisphere	$\dfrac{2}{3}\pi {r^3}$
Cylinder	$\pi {r^2}h$
Cone	$\dfrac{1}{3}\pi {r^2}h$