A cone with radius 9 cm has the same surface area as a cylinder with a radius of 6 cm and height 18 cm. What is the height of the cone to the nearest tenth?

Question

asked Feb 16, 2024 145k views

1 Answer

HannahS · Answer 1 · 2024-02-20T11:26:32+0000

Answer: 3.5 cm

Explanation:

SA for cone =
$\pi$ rs +
$\pi$ r² r=radius=9 s=slant height (not height)

A(cone) = 9
$\pi$ s + 81
$\pi$

SA for a cylinder = 2
$\pi$ rh +2
$\pi r^(2)$ r=6 h = 18

A(cyl) = 2(
$\pi$ )(6)(8) + 2(
$\pi$ )6²

= 96
$\pi$ + 72
$\pi$

=168
$\pi$

Set the 2 areas equal to each other to solve for slant height

9
$\pi$ s + 81
$\pi$ = 168
$\pi$

9
$\pi$ s=87
$\pi$

s=87/9

this is slant height, now you use pythagorean to solve for h

(87/9)²=9²+h²

h=3.5