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

A right cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is:3 : 52 : 53 : 11 : 3

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.

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? A. The volume of the cone is 1313 of the volume of the cylinder. B. The volume of the cone is 1414 of the volume of the cylinder. C. The cylinder’s volume is 2 times the volume of the cone. D. The cylinder’s volume is 8 times the volume of the cone.

The lateral surface area of cone A is equal to the lateral surface area of cylinder B.A.TrueB.FalseSUBMITarrow_backPREVIOUS

A prism has three times the volume of a pyramid with the same base and altitude.A.TrueB.False