What is the shape of the cross section taken perpendicular to the base of a cone?

Circle

Rectangle

Square

Triangle

The cross-sectional areas of a right triangular prism and a right cylinder are congruent. The right triangular prism has a height of 6 units, and the right cylinder has a height of 6 units. Which conclusion can be made from the given information?

The volume of the triangular prism is half the volume of the cylinder.

The volume of the triangular prism is twice the volume of the cylinder.

The volume of the triangular prism is equal to the volume of the cylinder.

The volume of the triangular prism is not equal to the volume of the cylinder.

Paul and Manuel disagree on the reason why the volumes of cone W and square pyramid X are related. Examine their arguments. Which statement explains whose argument is correct and why?

Paul

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 (d) = (12) = 37.68 cm2. The volume of cone W is 1/3(area of base)(h) =1/3(37.68)(5) = 62.8 cm3. The volume of square pyramid X is 1/3(area of base)(h) = 1/3 (37.68)(5) = 62.8 cm3.

Maunels

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 1/3 (r2) = (62) = 113.04 cm2. The volume of cone W is(area of base)(h) =1/3(113.04)(5) = 188.4 cm3. The volume of square pyramid X is 1/3 (area of base)(h) = 1/3(113.04)(5) = 188.4 cm3.

Paul'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