Question

if the height of the cylinder with a radius of 12 cm and a height of 20 cm has the same volume as a cone with a radius of 8 cm. what is the height of the cone​

Answer 1

Answer:

$\large\boxed{H=135\ cm}$

Step-by-step explanation:

The formula of a volume of a cylinder:

$V=\pi r^2H$

r - radius

H - height

We have the radius r = 12cm and the height H = 20cm. Substitute:

$V=\pi(12^2)(20)=\pi(144)(20)=2880\pi\ cm^3$

The formula of a volume of a cone:

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

r - radius

H - height

We have the radius r = 8cm and the volume V = 2880πcm³. Substitute:

$\dfrac{1}{3}\pi(8^2)H=2880\pi\qquad\text{divide both sides by}\ \pi\\\\\dfrac{1}{3}(64)H=2880\qquad\text{multiply both sides by 3}\\\\64H=8640\qquad\text{divide both sides by 64}\\\\H=135\ cm$