Cavalieri's Principle and Volume of Composite Figures

Question 1

What is the cross-sectional area of the shaded ring?

Revolt · Accepted Answer

πr2 – πb2, or π(r2 – b2)

Question 2

Complete the steps to determine the volume of space in the cylinder that is not being taken up by the sphere.

Revolt · Accepted Answer

Calculate the volume of the cylinder to the nearest tenth. V = cm3: 76.4; Calculate the volume of the sphere to the nearest tenth. V = cm3: 51.0; Determine the of the volumes to find the leftover space. The volume of space in the cylinder that is not being taken up by the sphere is about cm3.: difference; Determine the of the volumes to find the leftover space. The volume of space in the cylinder that is not being taken up by the sphere is about cm3.: 25.4

Question 3

22.2✔ 51.066.5

Revolt · Accepted Answer

✔ 51.0

Question 4

✔ differenceproductsum

Revolt · Accepted Answer

✔ difference

Question 5

✔ 25.428.334.4

Revolt · Accepted Answer

✔ 25.4

Question 6

The cross-sectional area of the shaded circle is πx2. Using the Pythagorean theorem for the right triangle, we get x2 + b2 = r2. Now solve for x2 and substitute it into the area expression.What is the result?

Revolt · Accepted Answer

π(r2 – b2)

Question 7

What is the formula for the volume of a hemisphere?

Revolt · Accepted Answer

πr3

Question 8

Which expressions represent the volume of the shaded composite figure? Check all that apply.

Revolt · Accepted Answer

π(33) – π(1.53); 36π – 4.5π; 31.5π

Question 9

Complete the steps to determine the volume of space in the cylinder that is not being taken up by the sphere.

Revolt · Accepted Answer

✔ 76.4; Calculate the volume of the cylinder to the nearest tenth. V = cm3: 76.4; Calculate the volume of the sphere to the nearest tenth. V = cm3: 51.0; Determine the of the volumes to find the leftover space. The volume of space in the cylinder that is not being taken up by the sphere is about cm3.: difference; Determine the of the volumes to find the leftover space. The volume of space in the cylinder that is not being taken up by the sphere is about cm3.: 25.4

Cavalieri's Principle and Volume of Composite Figures Answers

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