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?
Question
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?
Solution
The volume of the cylindrical-shaped container is three times the volume of the cone. This is because the formula for the volume of a cylinder is V = πr²h, and the formula for the volume of a cone is V = 1/3πr²h. Given that the base and height of the cone and cylinder are congruent, the only difference between their volumes is the 1/3 factor in the formula for the volume of a cone. Therefore, it takes three times as much soil to fill the cylinder as it does to fill the cone.
Similar Questions
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.
The solids below have the same base and the same height. If the cone is filled with water and poured into the cylinder, how much of the cylinder will be filled?Group of answer choices1/31/22/33/4
A cone has one-third times the volume of a cylinder with the same base and altitude.A.TrueB.False
We have a cone with radius 2 and height 6. We are filling it with water. What would be the volume of water if we fill it up to height 3?
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