Question

The volume of a cylinder is 3960 cm its curved surface area is 1320 .Find the radius of the base and height of the cylinder

Answer 1

Answer:

Step-by-step explanation:

volume of cylinder = 3960 (given)...(i)

πr^2h = 3960 cm (given)

curved surface area of cylinder = 2πrh

2πrh=1320 (given)

πrh = 660

rh = 660×7/22

rh = 210

h= 210/r.......(ii)

putting value of eqn (ii) in eqn(i)

r^2× 210/r = 3960×7/22

210r = 1260

r = 1260/210

r= 6 cm

putting value of r in eqn(ii)

h =210/r

h= 210/6 = 35 cm

hence radius = 6cm and height = 35cm

Answer 2

Answer:

$\huge\boxed{\green{r=6\:cm}}\\\\\huge\boxed{\red{h=35\:cm}}$

Step-by-step explanation:

Volume = 3960 cm³

Volume is the amount of mass contained in the body .

Volume = area of cross section × height .

We know that the volume of a cylinder is given by the formula π r² h .

So we can write that :

π r² h = 3960 cm³ .......( 1 )

Curved surface area = perimeter of cross section × height

= 2 π r h

2 π r h = 1320 cm² .....( 2 )

Divide ( 1 ) by ( 2 ) :

⇒ ( π r² h ) / ( 2 π r h ) = 3960 / 1320

⇒ r / 2 = 3

⇒ r = 6

Hence the radius is 6 cm .

Height = ?

We know from 2 that :

2 π r h = 1320 cm²

⇒ 2 × 22/7 × 6 × h = 1320

⇒ 44/7 × 6 × h = 1320

⇒ h = 1320 × 7/( 44 × 6 )

⇒ h = 1320 × 7/264

⇒ h = 5 × 7

⇒ h = 35

The height is 35 cm .