Question

Four times the area of the curved surface of a cylinder is equal to 6 times the sum of the area of its bases. it its height is 12 cm, Find its curved surface area

Answer 1

Curved Surface Area= 2πrh sq.cm
Area of the base = πr² sq.cm.
Sum area of the base= πr²+πr²= 2πr²sq.cm
A.T.Q
4(2πrh)= 6×2πr²
8πrh=12πr²
2h=3r
2×12=3r
r=8cm.
Curved Surface Area=2πrh
= 2×22/7×8×12
=4224/7
= 603.42 sq.cm

Answer 2

Given: Four times the area of the curved surface of a cylinder is equal to 6 times the sum of the area of its bases. Its height is 12 cm.

To find: Its curved surface area

Solution:

The curved surface area of a cylinder can be calculated by using the following formula.

$(Area)_{curved} = 2\pi rh$

Here, r is the radius of the cylinder and h is the height of the cylinder. Now, the area of the bases is calculated as

$(Area)_{bases} = \pi *r^{2}$

According to the question, the following equation can be formed.

$4(2\pi rh) = 6 (\pi r^{2} +\pi r^{2} )$

$4(2\pi r(12)) = 6 (\pi r^{2} +\pi r^{2} )$

$96r=12r^{2}$

$r = 8 cm$

Thus, the curved surface area can be calculated as follows.

$(Area)_{curved} = 2(\frac{22}{7} ) (8)(12)$

                    $= 603.43 cm^{2}$

Therefore, the curved surface area is 603.43 cm².