Cavalieri's Principle and Volume of Composite Figures

Question 1

Look at the two stacks of coins. Each stack contains the same type and number of coins.Make a conjecture. How do the stacks compare? Check all that apply.

Revolt · Accepted Answer

The two stacks are the same height.; The area of a coin face in one stack is the same as the area of a coin face that lies in the same horizontal plane.; The two stacks have equal volume.

Question 2

Is Erik’s statement correct? Why or why not?

Revolt · Accepted Answer

No, the heights of the cones are not the same, so Cavalieri’s principle does not apply.

Question 3

If the prisms are the same height, how do their volumes compare?

Revolt · Accepted Answer

The volumes are equal, because the heights are equal and the horizontal cross-sectional areas at every level are also equal.

Question 4

Complete the steps to find the width of the prism.

Revolt · Accepted Answer

Find the volume of the prism.V = m3: 40x; Find the volume of the cylinder.V = m3: 72; Set the volumes equal to each other and solve for x. Round to the nearest tenth. x = m: 5.7

Question 5

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

Revolt · Accepted Answer

[image 1] (7)(12)(10) – [image 2] π(32)(10); 280 – 30π

Question 6

Complete the statements to determine the amount of BTUs needed to properly cool Arthur's apartment.

Revolt · Accepted Answer

The total volume of the apartment is ft3.: 2,160; An hourly rating of 2.5 BTUs per cubic foot is required, so .: multiply the total volume by 2.5; Arthur needs an air conditioner that will provide BTUs to properly cool his apartment.: 5,400

Question 7

Complete the statements to determine the amount of BTUs needed to properly cool Arthur's apartment.

Revolt · Accepted Answer

✔ 2,160; The total volume of the apartment is ft3.: 2,160; An hourly rating of 2.5 BTUs per cubic foot is required, so .: multiply the total volume by 2.5; Arthur needs an air conditioner that will provide BTUs to properly cool his apartment.: 5,400

Question 8

divide 2.5 by the total volumedivide the total volume by 2.5✔ multiply the total volume by 2.5

Revolt · Accepted Answer

✔ multiply the total volume by 2.5

Question 9

X 4,000✔ 5,4006,500

Revolt · Accepted Answer

✔ 5,400

Cavalieri's Principle and Volume of Composite Figures Answers

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