If the radius of a right circular cylinder is increased by 10 percent while its height remains constant, what is the percentage increase in its volume?
If the radius of a right circular cylinder is increased by 10 percent while its height remains constant, what is the percentage increase in its volume?
यदि एक लंब वृत्तीय बेलन की त्रिज्या में 10 प्रतिशत की वृद्धि कर दी जाए और उसकी ऊँचाई स्थिर रहे, तो उसके आयतन में कितने प्रतिशत की वृद्धि होगी?
Detailed Solution & Logic
Correct Answer:
21
Solution:
Volume of a cylinder $V = \pi r^2 h$.
If the radius increases by $10%$, the new radius becomes $1.1r$.
Height remains the same.
New volume
$V' = \pi (1.1r)^2 h$
$V' = \pi (1.21r^2)h$
$V' = 1.21 \pi r^2 h$
So the volume becomes $1.21V$.
Increase in volume
$= 1.21V - V = 0.21V$
Percentage increase
= 21%
Answer: $21%$ increase in volume.
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