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

Question

asked Jul 9, 2023 143k views

1 Answer

Yuen Tong · Answer 1 · 2023-07-13T04:07:22+0000

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

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