Problem

Solid A is a cylinder with diameter \(10~\text{ft}\) and height \(7~\text{ft}\). Solid B is a \(9~\text{ft}~by~9~\text{ft}~by~7~\text{ft}\) prism. Calculate \(\text{both}~\text{base}~\text{areas}~\text{and}~\text{volumes}\), and compare the volumes.

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Solid A: base area = π(10)² = 100π ft², so VA = (100π)(7) = 700π ft³ ≈ 2199.1 ft³. Solid B: base area = 9×9 = 81 ft², so VB = (81)(7) = 567 ft³. Therefore, Solid A has more volume than Solid B.

Solid A: base area = π(5)² = 25π ft², so VA = (25π)(7) = 175π ft³ ≈ 549.8 ft³. Solid B: base area = 9×9 = 81 ft², so VB = (81)(7) = 567 ft³. Therefore, the solids have the same volume because both heights are 7 ft.

Solid A: base area = π(5)² = 25π ft², so VA = (25π)(7) = 175π ft³ ≈ 549.8 ft³. Solid B: base area = 9×9 = 81 ft², so VB = (81)(7) = 567 ft³. Therefore, Solid A has less volume than Solid B.

Solid A: base area = π(5)² = 25π ft², so VA = (25π)(7) = 175π ft³ ≈ 549.8 ft³. Solid B: base area = 9+9 = 18 ft², so VB = (18)(7) = 126 ft³. Therefore, Solid A has more volume than Solid B.

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Solid A is a cylinder with diameter \(10~\text{ft}\) and height \(7~\text{ft}\). Solid B is a \(9~\text{ft}~by~9~\text{ft}~by~7~\text{ft}\) prism. Calculate \(\text{both}~\text{base}~\text{areas}~\text{and}~\text{volumes}\), and compare the volumes.

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