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
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.