Question

Volume and curved surface of a cylinder are 24750 cm3 and 3300 cm2 respectively.
Find the height and radius of the base of cylinder.​

Answer 1

Answer:

Curved surface area =3300cm

3

volume =24750cm

3

CSA =2πrh

Let the height be h and radius be r

Also, 3300=2π×r×h

h=

2πr

3300

__ (1)

Also,

Volume =πr

2

h

24750=π×r

2

×

2πr

3300

24750=

2

3300×r

24750=1650×r

r=

1650

24750

Radius =15cm

CSA = 2πrh

3300=2π×15×h

h=

2π×15

3300

h=35cm

height =35cm

Answer 2

Answer ::

• The radius of cylinder = 15cm.
• The height of cylinder = 35cm.

Step-by-step explanation ::

To Find :-

• The height of the cylinder
• The radius of the base of cylinder

Solution :-

Let the radius be r centimetres and the height be h centimetres,

$\sf{2\pi \: h = 3300 \: \: \: \: \: \: . \: . \: .(i)}$

$\sf{\pi \: {r}^{2}h = 24750 \: \: \: \: \: \: \: \: . \: . \: . \: (ii)}$

Now, on dividing ( ii ) by ( i ),

$\sf{ \dfrac{\pi \: {r}^{2}h}{2\pi \: rh} = \dfrac{24750}{3300}}$

$\sf{ \leadsto \: \dfrac{\pi \: {r}^{2}h}{2\pi \: rh} = \dfrac{24750}{3300}} \\ \\ \\ \sf{ \leadsto \: \dfrac{ \cancel{\pi} \: {r}^{2}h}{2 \cancel{\pi} \: rh} = \dfrac{24750}{3300}} \\ \\ \\ \sf{ \leadsto \: \dfrac{ \cancel{{r}^{2}}h}{2 \: \cancel{r}h} = \dfrac{24750}{3300}} \\ \\ \\ \sf{ \leadsto \: \dfrac{r \: \cancel{h}}{2 \: \cancel{h}} = \dfrac{24750}{3300}} \\ \\ \\ \sf{ \leadsto \: r = \dfrac{2 \times 24750}{3300}} \\ \\ \\ \sf{ \leadsto \: r = \dfrac{49500}{3300}} \\ \\ \\ \sf{ \leadsto \: r = \cancel{ \dfrac{49500}{3300}}} \\ \\ \\ \sf{ \leadsto \: r = 15} \: \: \: \: \: \: \: \bigstar$

Now, height of the cylinder is,

Putting r = 15 in ( i ),

$\sf{ \leadsto \: 2 \times \dfrac{22}{7} \times 15 \times h = 3300} \\ \\ \\ \sf{ \leadsto \: \dfrac{22 \times 15 \times 2}{7} \times h = 3300} \\ \\ \\ \sf{ \leadsto \: \dfrac{660}{7} \times h = 3300} \\ \\ \\ \sf{ \leadsto \: h = \dfrac{3300 \times 7}{660}} \\ \\ \\ \sf{ \leadsto \: h = \dfrac{23100}{660}} \\ \\ \\ \sf{ \leadsto \: h = \cancel{\dfrac{23100}{660}}} \\ \\ \\ \sf{ \leadsto \: h = 35} \: \: \: \: \: \bigstar$

Hence, the height of cylinder is 35cm.