Question

If ‘d’ is the diameter of a sphere, then its volume is:
(a) \[\dfrac{2}{3}\pi {{d}^{3}}\]
(b) \[\dfrac{1}{6}\pi {{d}^{3}}\]
(c) \[\dfrac{4}{3}\pi {{d}^{3}}\]
(d) \[\dfrac{1}{24}\pi {{d}^{3}}\]

Answer 1

Hint: To solve this question, you must know the formula for the volume of a sphere. Here, you simply write the formula of the volume in terms of the diameter and solve it to get the answer. The volume of the sphere is given as \[V=\dfrac{4}{3}\pi {{r}^{3}},\] where r is the radius of the sphere.

Complete step-by-step answer:
Let the diameter of the sphere be ‘d’. We know that the formula for the volume of a sphere is given by:
\[\text{Volume of sphere}=\dfrac{4}{3}\pi {{r}^{3}}\]
where r is the radius of the sphere. Here, \[r=\dfrac{d}{2}.\]
Now, we will substitute this value of r in the formula.
\[\text{Volume of sphere}=\dfrac{4}{3}\pi {{\left( \dfrac{d}{2} \right)}^{3}}\]
Opening the bracket and solving accordingly we get,
\[\text{Volume of sphere}=\dfrac{4}{3}\times \pi \times {{\dfrac{d}{8}}^{3}}\]
Canceling the terms in the above expression, we get,
\[\text{Volume of sphere}=\dfrac{\pi {{d}^{3}}}{3\times 2}=\dfrac{\pi {{d}^{3}}}{6}\]
\[\text{Volume of sphere }=\dfrac{1}{6}\pi {{d}^{3}}\]
Hence, option (b) is the right answer.

Note: Do not get confused between the formula of the circle and a sphere. A circle is a 2D shape that does not have volume, whereas a sphere is a 3D shape which has the volume, \[\text{Volume }=\dfrac{4}{3}\pi {{r}^{3}},\] where r is the radius of the sphere.