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The radius of the base of a right circular cone is increased by 15% keeping the height fixed. The volume of the cone will be increased by
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A) 30% |
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B) 31% |
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C) 32.25% |
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D) 34.75% |
Correct Answer:
| A) 30% |
Description for Correct answer:
Let the fixed height of a right circular cone is h and initial radius is r.
Then, initial volume of cone, \( \Large V_{1} = \frac{1}{3} \pi r^{2}h \)
After increasing 15% radius of a cone
= \( \Large \left(r + \frac{3r}{20}\right) = \frac{23}{20}r \)
New volume becomes, \( \Large V_{2} = \frac{1}{3} \pi \left(\frac{23}{20}\right)^{2}r^{2}h \)
Therefore, Increasing percentage = \( \Large \left(\frac{V_{2} - V_{1}}{V_{1}}\right) \times 100 \)
= \( \Large \frac{\frac{1}{3} \pi r^{2}h}{\frac{1}{3} \pi r^{2}h}\{ \left(\frac{23}{20}\right) ^{2} - 1 \} \times 100 \)
= \( \Large \left(\frac{23}{20}+1\right) \left(\frac{23}{20}-1\right) \times 100 \)
= \( \Large \frac{43}{20} \times \frac{3}{20} \times 100 \)
= 32.25%
Let the fixed height of a right circular cone is h and initial radius is r.
Then, initial volume of cone, \( \Large V_{1} = \frac{1}{3} \pi r^{2}h \)
After increasing 15% radius of a cone
= \( \Large \left(r + \frac{3r}{20}\right) = \frac{23}{20}r \)
New volume becomes, \( \Large V_{2} = \frac{1}{3} \pi \left(\frac{23}{20}\right)^{2}r^{2}h \)
Therefore, Increasing percentage = \( \Large \left(\frac{V_{2} - V_{1}}{V_{1}}\right) \times 100 \)
= \( \Large \frac{\frac{1}{3} \pi r^{2}h}{\frac{1}{3} \pi r^{2}h}\{ \left(\frac{23}{20}\right) ^{2} - 1 \} \times 100 \)
= \( \Large \left(\frac{23}{20}+1\right) \left(\frac{23}{20}-1\right) \times 100 \)
= \( \Large \frac{43}{20} \times \frac{3}{20} \times 100 \)
= 32.25%
Part of solved Volume and surface area questions and answers : >> Elementary Mathematics >> Volume and surface area
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