A cylinder with a radius of 1 cm and a height of 21 cm has the same volume as a cone with a height of 7 cm. What is the radius of the cone? A) 3 cm B) 5 cm C) 7 cm D) 9 cm

Question

asked Jun 2, 2020 47.4k views

2 Answers

Rodmar Conde · Answer 1 · 2020-06-06T06:05:31+0000

Answer:

Explanation:

The formula of a volume of a cylinder:

$V=\pi r^2H$

r - radius

H - height

We have r = 1cm and H = 21cm. Substitute:

$V=\pi(1^2)(21)=21\pi\ cm^3$

The formula of a cone:

$V=(1)/(3)\pi r^2H$

r - radius

H - height

We have V = 21π cm³ and H = 7cm. Substitute:

$(1)/(3)\pi(r^2)(7)=21\pi$ divide both sides by π

(1)/(3)(7)(r^2)=21 divide both sides by 7

(1)/(3)r^2=3 multiply both sides by 3

$r^2=9\to r=\sqrt9\\\\r=3\ cm$