Question : The radius and the height of the cone are each increased by 20%. Then the volume of the cone increases by:
Option 1: 20%
Option 2: 20.5%
Option 3: 62%
Option 4: 72.8%

Question

Question : The radius and the height of the cone are each increased by 20%. Then the volume of the cone increases by:

Option 1: 20%

Option 2: 20.5%

Option 3: 62%

Option 4: 72.8%

Team Careers360 · Accepted Answer

Correct Answer: 72.8%

Solution : Given: The radius and the height of the cone are each increased by 20%.
Let the radius and height of the cone be 10 m.
When radius and height is increased by 20%, then new height and radius = $\frac{120}{100} imes10$ = 12 m
Volume of cone before increment $=\frac{1}{3}\pi r^2 h$
$=\frac{1}{3}\pi imes 10^2 imes 10 =\frac{1000}{3}\pi$
Volume of cone after increment $=\frac{1}{3}\pi r^2 h$
$=\frac{1}{3}\pi imes 12^2 imes 12 =\frac{1728}{3}\pi$
Change in percentage = $\frac{ ext{Volume after increment}- ext{Volume before increment}}{ ext{Volume before increment}} imes100$
= $\frac{\frac{1728}{3}\pi-\frac{1000}{3}\pi}{\frac{1000}{3}\pi} imes 100$
= $\frac{\frac{(1728-1000)}{3}\pi}{\frac{1000}{3}\pi} imes 100$
= $\frac{728}{1000} imes 100$
= $72.8$%
Hence, the correct answer is 72.8%.

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Question : The radius and the height of the cone are each increased by 20%. Then the volume of the cone increases by:Option 1: 20%Option 2: 20.5%Option 3: 62%Option 4: 72.8%

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Question : The radius and the height of the cone are each increased by 20%. Then the volume of the cone increases by:
Option 1: 20%
Option 2: 20.5%
Option 3: 62%
Option 4: 72.8%