Question

If the radius of a cylinder is doubled keeping it's lateral surface area the same,then what is its height?

Answer 1

$\bold\red{GiveN:-}$

★ Initial radius :- r cm

★ Final radius :- 2r cm

★ Initial Height :- h cm

★ Let final Height :- H cm

★ Lateral surface area :- 2πrh

$\bold\red{SolutioN:-}$

There is no change in LSA,

LSA of initial radius = LSA of final radius

2πrh = 2π(2r)H

$\dfrac{rh}{(2r)}$ = H

$\dfrac{h}{2}$ = H

_________________________

Answer 2

$\large\underline\mathtt\color{blue}{Given:-}$

Initial radius $\implies$ r

Final radius $\implies$ 2r

Initial height $\implies$ h

final height$\implies$H

∴ Lateral surface area of the cylinder =2πrh

$\orange{\bold{\underline{\underline{step\:by\: step \:explanation:-}}}}$

Now.,

$\implies$ 2πrh

$\implies \:2\pi(2r) \times h$

$\implies \: \frac{rh}{(2r)} = h$

$\implies \cancel \frac{rh}{2r} = \frac{h}{2}$

$\blue{\bold{\underline{\underline{Be brainly}}}}$