Question

The volume and curved surface area of cylinder is 2310cm³ and 660cm² respectively. Find Its radius and height.​

Answer 1

is given volume of a cylinder =1650cm

πr

2

h=1650 ...(1)

It is given that curved surface area of cyliner =600cm

2πrh=660cm ...(2)

On solving (1) & (2)

2

r

=

660

1650

r=

330

1650

r=5cm

Substitute r=5 in (2), we get

2πrh=660

2.

7

22

×5×h=660

2×22×5×h=660×7

22×h=4620

h=

220

4620

h=21cm

∴ radius of cylinder =5cm

Height of the cylinder =21cm

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Answer 2

$\sf\colorbox{pink}{Answer }$

Curved surface area of the cylinder = 2πrh =660 cm2 ... (1)

Volume of the cylinder = πr2h =1650 cm3 ... (2)

From (1) and (2), we can calculate the radius (r) and the height of cylinder (h).

We know the volume of the cylinder, i.e. 1650 cm3

∴ 1650 = πr2h

h=1650πr2

Substituting h into (1):

660 = 2πrh

h=1650πr2

660r = 2(1650)

r = 5 cm

h=1650πr2

=1650227×52=21cm.

Hence, the radius and the height of the cylinder are 5 cm and 21 cm, respectively.