If the radius of cylinder is doubled, but height is reduced by 50%. What is the percentage change in volume?a)100%b)150%c)125%d)175%e)None of theseCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

R1/R2 = R/2R & H1/H2 = H/H/2
Original Volume = πr²h
New Volume = π(2r)²h/2
Change in Volume = (2 – 1)/1 * 100 = 100

Answer

Given:
Radius of cylinder is doubled
Height is reduced by 50%

To find:
Percentage change in volume

Solution:
Let's assume the initial radius of the cylinder is 'r' and the initial height is 'h'.

Step 1: Calculate the initial volume of the cylinder
The formula to calculate the volume of a cylinder is V = πr^2h.
So, the initial volume of the cylinder is V1 = πr^2h.

Step 2: Calculate the new radius and height
According to the given information, the radius is doubled. So, the new radius is 2r.
The height is reduced by 50%, which means it is reduced to half. So, the new height is h/2.

Step 3: Calculate the new volume of the cylinder
Using the same formula, the new volume of the cylinder is V2 = π(2r)^2(h/2) = 4πr^2(h/2) = 2πr^2h.

Step 4: Calculate the percentage change in volume
The percentage change in volume can be calculated using the formula:
Percentage change = ((V2 - V1) / V1) * 100

Substituting the values, we get:
Percentage change = ((2πr^2h - πr^2h) / πr^2h) * 100
Percentage change = (πr^2h / πr^2h) * 100
Percentage change = 100%

Therefore, the percentage change in volume is 100%.

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