Question 1
The prism shown in the diagram has a volume of 39 units. What is the volume of the pyramid? Explain your reasoning.

Question 2
Consider this cone and pyramid, which have the same height, h. Planes parallel to the base cut through each solid at equal
heights, as shown.

Part A
What is the approximate area of each cross section of the cone and pyramid?
Type the correct answer in each box. Use numerals Instead of words.

Part B
Consider your results from part A. What conclusion can you draw about the volumes of the cone and pyramid? Explain
your reasoning.

Part C
The volume of the pyramid is one-third of the area of its base multiplied by its height, which is 144/3 pi h cubic units. Using
this measurement and your answer from part B, derive a formula for the volume of a cone.

Question

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Respuesta :

akposevictor akposevictor · Answer 1 · 2022-04-25T14:44:39+02:00

The volume of the cone and pyramid are the same.

Formula for volume of cone = ⅓(144π × h)

Volume of cone = ⅓[πr² × height of cone)

Volume of triangular pyramid = ⅓[(½bh × height of pyramid)]

Also note the following:

Area of a circle = πr²

Area of a triangle = ½bh

Part A:

Area of circle 1 = πr² = π(12²) = 144π units²

Area of circle 2 = πr² = π(6²) = 36π units²

Area of circle 3 = πr² = π(3²) = 9π units²

Area of triangle 1 = ½(24)(12π) = 144π units²

Area of triangle 2 = ½(12)(6π) = 36π units²

Area of triangle 3 = ½(6)(3π) = 9π units²

Part B: Based on our results in part A, the volumes of the cone and pyramid, having the same height are the same.

Part C:

Volume of pyramid = ⅓(144π × h)

Using this measurement and our conclusion in part B:

Formula for the Volume of a cone = ⅓(144π × h)

Learn more about the volume of cone and pyramid on:

https://brainly.com/question/16017622