Question

the total surface area of a cylinder is 2464 Sq cm . the height and radius of the cylinder are equal .find the radius of thebase ofthe cylinder

Answer 1

hi friend
here's your answer looking for

if the radius and the height of the cylinder are equal then,

let the height = radius = x

so,

total surface area = 2πr(r+h)

now,
$2\pi \: r(r + h) = 2464 \\ \\ 2\pi \: x(x + x) = 2464 \\ \\ 2\pi \: x(2x) = 2464 \\ \\ 4\pi \: {x}^{2} = 2464 \\ \\ 4 \times \frac{22}{7} \times {x}^{2} = 2464 \\ \\ {x }^{2} = \frac{2464 \times 7}{88} \\ \\ {x}^{2} = \frac{17248}{88} \\ \\ x = \sqrt{196} \\ \\ x = 14$
so, 14 cm will be radius of base

hope you are satisfied with my answer