If a cone-shaped water cup holds 23 cubic inches and has a radius of 1 inch, what is the height of the cup? Use 3.14 to for pi. Round your answer to the nearest hundredth. (4 points)

6.76 inches

18.56 inches

21.97 inches

23.00 inches

1 answer

The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.

In this case, the volume is given as 23 cubic inches and the radius is given as 1 inch. Plug these values into the formula and solve for h:

23 = (1/3)(3.14)(1^2)h
23 = (1/3)(3.14)(1)h
23 = (1.047)(h)
Simplify by multiplying:
23 = 1.047h

Divide both sides by 1.047:
h = 23/1.047
h ≈ 21.97 inches

Therefore, the height of the cup is approximately 21.97 inches.