Final answer:
To find the volume of a frustum of a right circular cone, you can use the formula V = πh/3 (R² + r² + Rr), where V is the volume, h is the height, R is the radius of the lower base, and r is the radius of the upper base. Substituting the given values into the formula, the volume of the frustum of the cone is 4511.385 cm³.
Step-by-step explanation:
To find the volume of a frustum of a right circular cone, we need to subtract the volume of the smaller cone from the volume of the larger cone. The formula for the volume of a frustum of a cone is:
V = πh/3 (R² + r² + Rr)
Where:
- V is the volume of the frustum of the cone
- π is a mathematical constant, approximately equal to 3.142
- h is the height of the frustum of the cone
- R is the radius of the lower base of the frustum of the cone
- r is the radius of the upper base of the frustum of the cone
Substituting the given values into the formula, we have:
V = 3.142 x 15/3 (23² + 11² + 23 x 11) = 3.142 x 5 (529 + 121 + 253) = 3.142 x 5 x 903 = 4511.385 cm³