Question

How to find the lateral area and total surface area of a cone? please include one(1) problem per question with solutions

Answer 1

we have that

the formula to calculate the surface area of a cone is equal to

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

where

r is the radius of the circular base

l is the slant height

the formula to calculate the lateral area is equal to

`LA=\pi\cdot r\cdot l`

that means

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

example

Find out the surface area and lateral area of a cone with

r=5 cm

h=10 cm

step 1

Find out the slant height (l)

Applying the Pythagorean Theorem

l^2=h^2+r^2

substitute given values

l^2=10^2+5^2

l^2=125

l=11.18 cm

step 2

Find out the lateral area

`LA=\pi\cdot r\cdot l`

substitute given values

`\begin{gathered} LA=\pi\cdot5\cdot11.18 \\ LA=55.90\pi\text{ cm2} \end{gathered}`

step 3

Find out the surface area

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

substitute values

`\begin{gathered} SA=55.90\pi+\pi\cdot5^2 \\ SA=55.90\pi+25\pi \\ SA=80.90\pi\text{ cm2} \end{gathered}`