Question

Eighth grade ) T.14 Volume of spheres QX7 What is the volume of this sphere? Use : 3.14 and round your answer to the nearest hundredth. 1 ft 4.186 cubic feet

Answer 1

We are asked to find the volume of the given sphere.

Recall that the volume of a sphere is given by

`V=(4)/(3)\cdot\pi\cdot r^3`

Where π is a constant and r is the radius of the sphere.

For the given problem, the radius is 1 ft

So, the volume of the sphere is

`\begin{gathered} V=(4)/(3)\cdot\pi\cdot r^3 \\ V=(4)/(3)\cdot3.14\cdot(1)^3 \\ V=(4)/(3)\cdot3.14\cdot1 \\ V=4.1867 \\ V=4.19\: ft^3\quad (\text{rounded to the nearest hundredth)} \end{gathered}`

Therefore, the volume of the given sphere is 4.19 cubic feet.

Example:

If the given radius is 18 feet then the volume of the sphere is

`\begin{gathered} V=(4)/(3)\cdot\pi\cdot r^3 \\ V=(4)/(3)\cdot3.14\cdot(18)^3 \\ V=(4)/(3)\cdot3.14\cdot5832 \\ V=24416.64\: \: ft^3 \end{gathered}`

Therefore, the volume of the sphere is 24416.64 cubic feet.