Question

If four times the sum of the areas of the two circular faces of a cylinder of height 8 cm is equal to twice the curved surface area, then the diameter of the cylinder is

(a) 4 cm (b) 8 cm (c) 2 cm (d) 6 cm​

Answer 1

EXPLANATION.

4 times the sum of the area of the two circular

faces of a cylinder of height = 8 cm.

equal to the twice the curved surface area

To find diameter of the cylinder.

According to the question,

Let the radius of cylinder = r

area of circular base of cylinder = πr²

Height of cylinder = 8 cm.

Curved surface area of cylinder

=> 2πrh

=> 2πr X 8 = 16πr

=> Therefore,

=> 4 X ( πr² + πr² ) = 2 X ( 2πrh)

=> 8πr² = 32πr

=> r = 4

=> diameter = 2 X radius

=> Diameter = 2 X 4 = 8 cm

Answer 2

Question:-

If four times the sum of the areas of the two circular faces of a cylinder of height 8 cm is equal to twice the curved surface area, then the diameter of the cylinder is?

Answer:-8

To Find:-

The diameter of the circle

let the value be "r"

Explanation:-

h = 8cm

$4( {\pi \gamma }^{2} + {\pi \gamma }^{2} ) = 2(2\pi \gamma h) \\ 4 {\pi \gamma }^{2} \times 2 = 32\pi \gamma \\ {r}^{2} \div r = 32\pi \div 8\pi \\ r = 4 \\</em></strong></h3><p><strong><em> d = 2 \times 4 \\ d = 8$

2nd opinion is the answer.

hope this helps you.