Knowee
Questions
Features
Study Tools

Cone W has a radius of 10 cm and a height of 5 cm. Square pyramid X has the same base area and height as cone W.Paul and Manuel disagree on how the volumes of cone W and square pyramid X are related. Examine their arguments. Which statement explains whose argument is correct and why?Paul ManuelThe volume of square pyramid X is three times the volume of cone W. This can be proven by finding the base area and volume of cone W, along with the volume of square pyramid X. The base area of cone W is π(r2) = π(102) = 314 cm2. The volume of cone W is (area of base)(h) = (314)(5) = 523.33 cm3. The volume of square pyramid X is (area of base)(h) = (314)(5) = 1,570 cm3. The volume of square pyramid X is equal to the volume of cone W. This can be proven by finding the base area and volume of cone W, along with the volume of square pyramid X. The base area of cone W is π(r2) = π(102) = 314 cm2. The volume of cone W is (area of base)(h) = (314)(5) = 523.33 cm3. The volume of square pyramid X is (area of base)(h) = (314)(5) = 523.33 cm3.Group of answer choicesPaul's argument is correct; Manuel used the incorrect formula to find the volume of square pyramid X.Paul's argument is correct; Manuel used the incorrect base area to find the volume of square pyramid X.Manuel's argument is correct; Paul used the incorrect formula to find the volume of square pyramid X.Manuel's argument is correct; Paul used the incorrect base area to find the volume of square pyramid X.

Question

Cone W has a radius of 10 cm and a height of 5 cm. Square pyramid X has the same base area and height as cone W.Paul and Manuel disagree on how the volumes of cone W and square pyramid X are related. Examine their arguments. Which statement explains whose argument is correct and why?Paul ManuelThe volume of square pyramid X is three times the volume of cone W. This can be proven by finding the base area and volume of cone W, along with the volume of square pyramid X. The base area of cone W is π(r2) = π(102) = 314 cm2. The volume of cone W is (area of base)(h) = (314)(5) = 523.33 cm3. The volume of square pyramid X is (area of base)(h) = (314)(5) = 1,570 cm3. The volume of square pyramid X is equal to the volume of cone W. This can be proven by finding the base area and volume of cone W, along with the volume of square pyramid X. The base area of cone W is π(r2) = π(102) = 314 cm2. The volume of cone W is (area of base)(h) = (314)(5) = 523.33 cm3. The volume of square pyramid X is (area of base)(h) = (314)(5) = 523.33 cm3.Group of answer choicesPaul's argument is correct; Manuel used the incorrect formula to find the volume of square pyramid X.Paul's argument is correct; Manuel used the incorrect base area to find the volume of square pyramid X.Manuel's argument is correct; Paul used the incorrect formula to find the volume of square pyramid X.Manuel's argument is correct; Paul used the incorrect base area to find the volume of square pyramid X.

...expand
🧐 Not the exact question you are looking for?Go ask a question

Solution

Manuel's argument is correct; Paul used the incorrect formula to find the volume of square pyramid X.

The volume of a cone is given by the formula V = 1/3πr²h, and the volume of a pyramid is given by the formula V = 1/3Bh, where B is the area of the base and h is the height. Since the base area and height of the cone and pyramid are the same, their volumes will also be the same. Paul incorrectly used the formula for the volume of a cylinder (V = Bh) to calculate the volume of the pyramid.

This problem has been solved

Similar Questions

A pyramid and a cone are both 10 centimeters tall and have the same volume. What statement must be true about the two solids?A.The cross-sections of the pyramid and cone are the same shape.B.The area of the cross-sections of the pyramid and cone are multiples of each other.C.The vertical cross-sections of the pyramid and cone at the same width must have the same area.D.The horizontal cross-sections of the pyramid and cone at the same height must have the same area.

A cylindrical-shaped container requires 12 cubic feet of soil to be considered full. If a cone with a congruent base and height requires 4 cubic feet of soil, which statement describes how the volumes of these two figures are related?

Find the volume of a pyramid with a square base, where the area of the base is 8, point, 7, m, squared8.7 m 2 and the height of the pyramid is 10, m10 m. Round your answer to the nearest tenth of a cubic meter.

Pyramid A is a square pyramid with a base side length of 18 inches and a height of 9 inches. Pyramid B has a volume of 3,136 cubic inches. How many times bigger is the volume of pyramid B than pyramid A? Give your answer as a percentage. Provide an explanation and proof for your answer to receive full credit.

A cone has one-third times the volume of a cylinder with the same base and altitude.A.TrueB.False

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.