Question

Find the total surface area of this cone.

Leave your answer in terms of .
15 cm
78 cm
SA = [ ? 17 cm?

Answer 1

in the right angle triangle,

p=15cm

b=8cm

`h = \sqrt{15 {}^(2) + 8 {}^(2) } \\ = √(125 + 64) \\ = √(289) \\ = 17cm \\ sa = \pi \: rl + b \\ = \pi \: 8 * 17 + \pi \: r {}^(2) \\ = 136\pi + 64\pi \\ = 200\pi`

Answer 2

SA = 200π cm²

Explanation:

The slant height l is the hypotenuse of the right triangle inside the cone

The triangle is an 8- 15- 17 ( Pythagorean triple ) with l = 17

Then

SA = πrl + πr²

=(π × 8 × 17) + (π × 8²)

= 136π + 64π

= 200π cm²