Question

find the height of a cylinder of currved surface 12cm square and radius 4cm?

Answer 1

Given Curved surface area of cylinder (C.S.A) = 12 sq. cm

Given radius of cylinder (r) = 4cm

Now as we know that C.S.A of cylinder is

2πrh

where h is the height of cylinder.

Therefore,

$2\pi rh = 12 \\ \\ = > \pi = \frac{22}{7} \\ \\ 2 \times \frac{22}{7} \times 4 \times h = 12 \\ \\ \frac{176}{7} h = 12 \\ \\ h = 12 \times \frac{7}{176} \\ \\ h = \frac{7}{44} \times 3 \\ \\ h = \frac{21}{44} \\ \\ h = 0.47$cm

$height \: = \frac{21}{44} \: or \: 0.47$cm

$verification \\ \\ 2\pi rh = 12 \\ \\ 2 \times 4 \times \frac{22}{7} \times \frac{21}{44} = 12 \\ \\ 22 \times 4 \times \frac{3}{22} = 12 \\ \\ 4 \times 3 = 12 \\ \\ 12 = 12$

Since L.H.S = R.H.S
Therefore the value of height is correct

HOPE IT WOULD HELP YOU

Answer 2

Curved Surface Area of a Cylinder = 12 cm²

Radius = 4 cm

2πrh = 12

$2 \times \frac{22}{7} \times 4 \times h = 12 \\ \\ \frac{176}{7} \times h = 12 \\ \\ h = 12 \times \frac{7}{176} = 0.47 cm$

The required height is 0.47 cm .