To find the area of the base of the model, we need to use the formula for the volume of a cone, which is:
V = (1/3) * π * r^2 * h
Where V is the volume, r is the radius of the base, h is the height.
Given that the volume is 586.7 cubic centimeters and the height is 22 cm, we can rearrange the formula to solve for the radius of the base:
586.7 = (1/3) * π * r^2 * 22
r^2 = 586.7 / (1/3) * π * 22
r^2 = 60.3
r = √60.3
r ≈ 7.77 cm
Now that we have the radius of the base, we can calculate the area of the base using the formula for the area of a circle:
A = π * r^2
A = π * 7.77^2
A ≈ π * 60.3
A ≈ 188.9 cm^2
Rounded to the nearest tenth, the area of the base of the model is 188.9 cm^2.
Therefore, none of the provided options are correct.
A model of a volcano that is 22 cm tall with a volume of 586.7 cubic centimeters. What is the area of the base of the model? Round the answer to the nearest tenth.
26.7 centimeters squared
80.0 centimeters squared
1,760.1 centimeters squared
4,302.5 centimeters squared
1 answer