Question

Find the volume of the sphere with d=163. Round your answer to the nearest tenth. Use 3.14 to represent pie.

Answer 1

To find the volume, V, of a sphere, the formula is

`\begin{gathered} V=(4)/(3)\pi r^3 \\ \text{Where r is the radius} \end{gathered}`

Given that the diameter, d, of the sphere is 163 units, the radius, r, is

`r=(d)/(2)`

Where d = 163, r will be

`r=(d)/(2)=(163)/(2)\text{ units}`

Substitute for r into the formula for the volume, V, of a sphere

`\begin{gathered} V=(4)/(3)\pi r^3 \\ \text{Where r}=(163)/(2)\text{ and }\pi\text{ is taken as 3.14} \\ V=(4)/(3)*3.14*((163)/(2))^3 \\ V=(4)/(3)*3.14*(4330747)/(8) \\ V=(3.14*4330747)/(3*2)=2266424.263333333 \\ V=2266424.3units^3\text{ (nearest tenth)} \end{gathered}`

Hence, the volume, V of the sphere is 2266424.3 unit³ (nearest tenth)