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

$V=\frac{1}{3}\cdot\pi\cdot r^2\cdot h$

we have

r=15 m

h=20 m

substitute

$\begin{gathered} V=\frac{1}{3}\cdot\pi\cdot15^2\cdot20 \\ \\ V=1,500\pi\text{ m3} \end{gathered}$

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

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