A solid cylinder is reduced in radius by 20% and increased in height by 50%. What net percentage change occurs in its volume?
A solid cylinder is reduced in radius by 20% and increased in height by 50%. What net percentage change occurs in its volume?
एक ठोस बेलन की त्रिज्या में 20% की कम कर दी जाती है और उसकी ऊँचाई में 50% की वृद्धि कर दी जाती है। उसके आयतन में कुल कितने प्रतिशत परिवर्तन होगा?
Detailed Solution & Logic
Correct Answer:
4% decrease
Solution:
Volume of a cylinder $V = \pi r^2 h$.
Radius is reduced by $20%$, so new radius
$= 0.8r$.
Height is increased by $50%$, so new height
$= 1.5h$.
New volume
$V' = \pi (0.8r)^2 (1.5h)$
$V' = \pi (0.64r^2)(1.5h)$
$V' = 0.96 \pi r^2 h$
$V' = 0.96V$
Change in volume
$= 0.96V - V = -0.04V$
Percentage change
= -4%
Answer: The volume decreases by 4%.
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