Question

The volume and curved surface area of a cylinder are equal numerically. If the height is 7/2 times the radius of the base, find the radius
The volume and curved surface area of a cylinder are equal numerically. If the height is 7/2 times the radius of the base, find the radius

Answer 1

Given ,

1. The volume and curved surface area of a cylinder are equal
2. The height is 7/2 times the radius of the base

Find : Radius (r)

Solution :

$curved \: surface \: area \: of \: cylinder = 2 \times \pi \: \times r \times h$

$volume \: of \: cylinder = \pi \: {r}^{2} h$

let,

1. h= height of cylinder
2. r = radius of cylinder

from above questions ,

h = 7/2 r

=> CSA OF cylinder = volume. of cylinder

=> 2πrh = πr²h

=> dividing both side by πrh

=> 2 = r

=> r = 2

Therefore ,

The radius is 2 unit

Answer 2

Given ,

1. The volume and curved surface area of a cylinder are equal
2. The height is 7/2 times the radius of the base
3. Find : Radius (r)

Solution :

$curve \: surface \: area \: of \: cylinder \: = 2\pi \: rh$

$volume \: of \: cylinder = \pi {r}^{2} h$

let,

1. h= height of cylinder
2. r = radius of cylinder

from above questions ,

• h = 7/2 r

=> CSA OF cylinder = volume. of cylinder

=>

$2\pi \: rh = \pi \: {r}^{2} h$

=> dividing both side by πrh

=>

$2 = r$

$r = 2$

Therefore ,

The radius is 2 unit