Question

What is the volume of the sphere with diameter 12 cm?

Answer 1

Hint: In this problem, we have to find the volume of the sphere. We know that the formula for the volume of the sphere is \[V=\dfrac{4}{3}\pi {{r}^{3}}\] cubic units. Here we have to substitute the value of r to find the volume of the sphere. Here we have diameter which is twice the radius, so we can divide the given diameter by 2 to get the value of radius which can be substituted to get the volume of the sphere.

Complete step-by-step answer:
Here we have to find the volume of the sphere.
We know that the formula for the volume of the sphere is,
Volume of the sphere, \[V=\dfrac{4}{3}\pi {{r}^{3}}\] cubic units …….. (1)
We are given a diameter of 12 cm.
We know that the radius is the half the diameter, where we should divide the given diameter by 2, we get
\[\Rightarrow r=\dfrac{12}{2}=6cm\]
We can now see that the radius is 6cm.
We can now substitute the radius value in (1), we get
\[\Rightarrow V=\dfrac{4}{3}\pi {{\left( 6 \right)}^{3}}\]
We can now simplify the above step, we get
\[\Rightarrow V=\dfrac{4}{3}\pi \left( 216 \right)=288\pi c{{m}^{3}}\]
Therefore, the volume of the sphere is \[V=288\pi c{{m}^{3}}\].

Note: We should always remember the formula for the volume of the sphere, \[V=\dfrac{4}{3}\pi {{r}^{3}}\] cubic units, where unit is very important. We should also remember that the diameter is twice the radius or the radius is half the diameter, so we can divide the given diameter by 2, to get the radius value.