Question

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?

Answer 1

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