Question

The formula for the volume of a cone is V=1/3(3.14)r^2(h) where V represents the volume, r represents the radius of the base, and h represents the height. What is the height of a cone with a volume of 66 cubic centimeters and a base with a radius of 3 centimeters?
F. 21 cm
G. 69.14 cm
H. 7 cm
J. 0.78 cm

Answer 1

The original formula for the volume of a cone is

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

O.K. You give the approximate value of pi in the formula.

$V=\dfrac{1}{3}\cdot3.14r^2h$

We have:

$V=66\ cm^3,\ r=3\ cm$

Substitute:

$\dfrac{1}{3}\cdot3.14\cdot3^2h=66\\\\3.14\cdot3h=66\\\\9.42h=66\ \ \ \ |:9.42\\\\h\approx7\ cm$

Answer: 7 cm.