The ratio of diameter and height of a right circular cylinder is 4 : 3. If diameter of the cylinder get reduced by 25% then its total surface area reduced to 318.5 square meter. What is the circumference of the base of the cylinder. (a) 28 pi m (b) 14 pi m (c) 35 pi m (d) 7 pi m (e) none of these

The ratio of diameter and height of a right circular cylinder is 4 : 3

1.	The ratio of diameter and height of a right circular cylinder is 4 : 3. If diameter of the cylinder get reduced by 25% then its total surface area reduced to 318.5 square meter. What is the circumference of the base of the cylinder. (a) 28 pi m (b) 14 pi m (c) 35 pi m (d) 7 pi m (e) none of these
Answer» Let the diameter be 4y and height be 3y Since the diameter = 4y => Radius = 4y/2 = 2Y So the total surface area = 2πr(h + r) => Total surface area = 2π2y(3y + 2y) => Total surface area = 4yπ(5y) => Total surface area = 20y²π Now the diameter is DECREASED by 25% => NEW diameter = 4y - 25% of 4y => $4y - \frac{25}{100} \times 4y \\ \\ = > 4y - \frac{1}{4} \times 4y \\ \\ = > 4y - y \\ \\ = > 3y$ New diameter = 3y => Radius = 3y/2 => Total surface area = $2\pi \frac{3y}{2} ( \frac{3y}{2} + 3y)$ $= > 3y\pi( \frac{3y + 6y}{2} )$ => $3y\pi( \frac{9y}{2} )$ $= > \frac{27 {y}^{2} }{2} \pi \\$ Given that new total surface area is 318.5 LESS than the old surface area => $20 {y}^{2} \pi - \frac{27 {y}^{2} }{2} \pi = 318.5 \\ \\ = > \frac{40y {}^{2} }{2} \pi - \frac{27 {y}^{2} }{2} \pi = 318.5 \\ \\ = > \frac{13y {}^{2} }{2} \pi = 318.5 \\ \\ = > {y}^{2} = 318.5 \times \frac{2}{13\pi} \\ \\ = > y {}^{2} = \frac{49}{\pi} \\ \\ = > y = \sqrt{ \frac{49}{\pi} } \\ \\ = > y = \frac{7}{ \sqrt{\pi} }$ Now radius = 2y => Radius = $2 \times \frac{7}{ \sqrt{\pi} } \\ \\ = > \frac{14}{ \sqrt{\pi} }$ Now circumference = 2πr => $2 \times \pi \times \frac{14}{ \sqrt{\pi} } \\ \\ = > 28 \sqrt{\pi}$ Answer is 28 √π Option a There should be 28 root pi though