A cylinder and a cone start with the same radius and height. The radius of the cone is then tripled, and the height of the cone is cut in half. The radius of the cylinder stays the same, but the height of the cylinder is doubled. Which change produces a greater increase in volume (i. e., which figure's volume increases by a larger factor) ? Justify your answer. Write "pi" for ^ and "r^2" for r squared

Question

Mathematics

Danielle Carlson

1 June, 19:02

A cylinder and a cone start with the same radius and height. The radius of the cone is then tripled, and the height of the cone is cut in half. The radius of the cylinder stays the same, but the height of the cylinder is doubled. Which change produces a greater increase in volume (i. e., which figure's volume increases by a larger factor) ? Justify your answer. Write "pi" for ^ and "r^2" for r squared

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Answers (1)

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June Donovan · Answer 1

Cone:

Original cone = (1/3) π (h) r^2

Changed cone = (1/3) π (h/2) (3r) ^2

= (1/2) (1/3) π (h) 9r^2

= (9/2) * Original cone

=4.5 * Original cone

Cylinder:

Original cylinder = π (h) r^2

Changed cylinder = π (2h) r^2

=2 * Original cylinder

Therefore the cone is the greatest relative increase in volume.