Question

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

Answer 1

Answer:

A 3cm

Step-by-step explanation:

Answer 2

Answer:

A) 3 cm

Step-by-step 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:

$V=\dfrac{1}{3}\pi r^2H$

r - radius

H - height

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

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

$\dfrac{1}{3}(7)(r^2)=21$         divide both sides by 7

$\dfrac{1}{3}r^2=3$         multiply both sides by 3

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