Question

A cone has a diameter of 3in The cone holds 12 cubic inches of water. To the nearest inch, what is the height of the cone

Answer 1

Area of the cone = 1/3 π r² h

12= 1/3 π (1.5)² h

36 = 2.25 π h

h = 36 ÷ 2.25π

h = 5 in

Answer: Height = 5 inches

Answer 2

To find the height of the cone, plug in all the numbers we know into the volume of a cone formula and solve for h.

Volume of a cone: 1/3($\pi$r²h)

1/3($\pi$1.5²h) = 12
Divide both sides by 1/3.

$\pi$1.5²h = 36
Divide both sides by $\pi$.

1.5²h = 11.46
Divide both sides by 1.5².

h = 5.09
Rounded to the nearest inch, 5.

The height of the cone is 5 inches.