Question

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 for pi and round your answer to the nearest hundredth.

Option 1: 6.76 inches
Option 2: 18.56 inches
Option 3: 21.97 inches
Option 4: 23.00 inches

Answer 1

To find the height of the cone-shaped water cup, we can use the formula for the volume of a cone and solve for h.

Step-by-step explanation:

To find the height of the cone-shaped water cup, we can use the formula for the volume of a cone: V = (1/3)πr²h, where V is the volume, π is approximately 3.14, r is the radius, and h is the height. Given that the volume is 23 cubic inches and the radius is 1 inch, we can substitute these values into the formula and solve for h:

23 = (1/3) × 3.14 × 1² × h

23 = 3.14 × h

h = 23 / 3.14

h ≈ 7.32

Rounding to the nearest hundredth, the height of the cup is approximately 7.32 inches. None of the provided options match this value exactly, so none of them are correct.