Question

Find the volume and total surface area of a right circular cone whose base radius is 15m and whose altitude is 20m.s

Answer 1

Find the volume and total surface area of a right circular cone whose base radius is 15m and

whose altitude is 20m

Part 1

Find out the volume

Remember that

the formula to calculate the volume of a right circular cone is

`V=(1)/(3)\cdot\pi\cdot r^2\cdot h`

we have

r=15 m

h=20 m

substitute

`\begin{gathered} V=(1)/(3)\cdot\pi\cdot15^2\cdot20 \\ \\ V=1,500\pi\text{ m3} \end{gathered}`

Part 2

Find out the surface area

the formula is equal to

`SA=\pi\cdot r^2+\pi\cdot L\cdot r`

where

L is slant height

Applying the Pythagorean Theorem

L^2=h^2+r^2

L^2=20^2+15^2

L^2=625

L=25 m

substitute given values

`\begin{gathered} SA=\pi\cdot15^2+\pi\cdot25\cdot20 \\ SA=725\pi\text{ m2} \end{gathered}`