Cavalieri's Principle and Volume of Composite Figures — Quiz

Question 6 • Geometry: Concepts and Connections

Which expression represents the volume, in cubic units, of the frustum?

Answer

1 third pi open paren 7 point 5 squared close paren 19 plus 1 third pi open paren 3 point 5 squared close paren 8

1 third pi open paren 7 point 5 squared close paren 19 minus 1 third pi open paren 3 point 5 squared close paren 8

1 third pi open paren 7 point 5 squared close paren 11 plus 1 third pi open paren 3 point 5 squared close paren 8

1 third pi open paren 7 point 5 squared close paren 11 minus 1 third pi open paren 3 point 5 squared close paren 8

Explanation

Find the frustum’s volume by subtracting the small cone from the original large cone. Using V = ⅓πr²h, the large cone has radius 7.5 and height 19, while the small cone has radius 3.5 and height 8. So the expression is ⅓π(7.5²)(19) − ⅓π(3.5²)(8), which is choice A.

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