The cylinder below has a volume of 785, and the cone has a volume of 314. Which explains which figure has the greater height?

The cylinder has a greater height because the bases are the same, but the cylinder has a greater volume.

The cylinder has a greater height because the volume of the cylinder is greater than twice the volume of the cone.

The cone has a greater height because the bases are the same, but the volume of the cylinder is less than 3 times the volume of the cone.

The cone has a greater height because the bases are the same, but the volume of the cylinder is less than 4 times the volume of the cone.

Question

Mathematics

Claudia Barron

22 November, 17:45

The cylinder below has a volume of 785, and the cone has a volume of 314. Which explains which figure has the greater height?

The cylinder has a greater height because the bases are the same, but the cylinder has a greater volume.

The cylinder has a greater height because the volume of the cylinder is greater than twice the volume of the cone.

The cone has a greater height because the bases are the same, but the volume of the cylinder is less than 3 times the volume of the cone.

The cone has a greater height because the bases are the same, but the volume of the cylinder is less than 4 times the volume of the cone.

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Answers (1)

Know the Answer?

Mina Morse · Answer 1

Given that both the cylinder have the same base area of 78.5 ft², to evaluate which one has the greatest height we use the formula:

V = (base area) * (height)

height of the cylinder with volume of 785 will be:

785=78.5h

thus

h=785/78.5

h=10 ft

Height of the cone with volume of 314 ft³ will be:

314=78.5h

thus

h=4

this implies that the cylinder has larger volume compared to the cone.

Answer:

The cylinder has a greater height because the volume of the cylinder is greater than twice the volume of the cone.