Volume of Spheres and Cavalieri's Principle

What is the volume of a sphere with the radius of 4 inches ? Use 3.14 for pi.

• 561.5 in³
• 267.9 in³
• 201 in³
• 803.8 in³

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Barney wanted to know how much ice cream he got in one scoop. The radius of a scoop is 2 inches. Find the volume. Use 3.14 for pi.

• 345.3 in³
• 33.5 in³
• 25.1 in³
• 50.2 in³

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Jack wants to know how much water a sphere can hold with a radius of 8 cm. Find the volume. Use 3.14 for pi.

• 83.6 cm³
• 2144.7 cm³
• 254 cm³
• 2220 cm³

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If a tennis ball has a diameter of 14, What is the volume of the tennis ball? Use 3.14 for pi.

• 345.8
• 523.6
• 1436
• 205.1

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a) Cavalieri’s Principle states that any two objects with the same cross sectional areas and heights must have the same volume.

• True

• False - the cross sectional areas are not relevant

• False - only the slant height is relevant

• False - even if they have the same cross sectional areas and heights, they cannot have the same volume.

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Based on Cavalieri's Principle, will the two prisms have the same volume?

• No, they will not be same. Although the heights are the same, the cross-sections are different shapes. 

• Yes, the heights of both prisms are the same and they have the same cross-sectional area. Therefore, they will have the same volume.
  

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