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Volumes Practice Test 3

Question : 3 of 40

Marks: +1, -0

Solution:

Concept:

When the radius is fixed, the volume of a cone is directly proportional to its height.

Explanation:

Let the original radius be

r

and original height be

h

Original volume:

V_1 = \frac{1}{3}\pi r^2 h

When the height is doubled, the new height is

2h

New volume:

V_2 = \frac{1}{3}\pi r^2 (2h) = 2\left(\frac{1}{3}\pi r^2 h\right) = 2V_1

Increase in volume:

V_2 - V_1 = 2V_1 - V_1 = V_1

Percentage increase:

\frac{V_1}{V_1} \times 100\% = 100\%

Answer:

The volume will be increased by

100\%

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