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Find the volume of a frustum of a right circular cone with a height of 15, a lower base radius of 23, and a top radius of 11.

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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

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