Question

Cam is making a party hat shown, in the shape of a cone for his birthday. The circumference of the part of his head where the hat will rest is 56 centimeters (cm). If the height of the hat is 25 cm, which of the following is closest to the volume of Cam's hat, measured in cubic centimeters (cm³)?

a) 22,000 cm³
b) 43,750 cm³
c) 55,000 cm³
d) 69,000 cm³

Answer 1

To find the volume of the party hat, use the formula for the volume of a cone and find the radius of the head. Then substitute the values into the volume formula and calculate the volume.

Step-by-step explanation:

To find the volume of the party hat, we can use the formula for the volume of a cone: V = 1/3 * π * r^2 * h. Given that the circumference of the head is 56 cm, we can find the radius (r) using the formula C = 2 * π * r. Solving for r, we get r = C / (2 * π) = 56 cm / (2 * π) ≈ 8.917 cm. Substituting the values into the volume formula: V = 1/3 * π * (8.917 cm)^2 * 25 cm ≈ 6604.78 cm³. Therefore, the closest volume to Cam's hat is 6604.78 cm³, which is closest to option b) 43,750 cm³.