The ratio of the diameter and height of the right circular cylinder is 4 : 3. If the diameter of the cylinder is reduced by 25%, then its total surface area is reduced to $318.5π\, m^2$. What is the circumference of the base of the cylinder?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $28π\, m^2$
Note: Given answer is as per NTA. However, there seems to be a mistake in the question. There appears to be a numerical inconsistency in the given value (318.5π), as the correct calculation does not match any of the options as explained below:
Let diameter : height = 4 : 3
So take diameter = 4x, height = 3x
⇒ radius = 2x
TSA = 2πr² + 2πrh
= 2π(2x)² + 2π(2x)(3x)
= 8πx² + 12πx²
= 20πx²
After 25% reduction in diameter
New diameter = 75% of 4x = 3x
⇒ new radius = 1.5x
New TSA =2π(1.5x)² + 2π(1.5x)(3x)
= 4.5πx² + 9πx²
= 13.5πx²
Using given condition
13.5πx² = 318.5π
⇒ x² = 318.5 ÷ 13.5
⇒ x² ≈ 23.59
Radius = 2x
Circumference = 2πr = 4πx
x ≈ √23.59 ≈ 4.85
So circumference ≈ 4π × 4.85 ≈ 19.4π
But this is not in the options.Hence, question/options mismatch exists.