Question

Find its radius of the base and its height.The radius and height of a cylinder are in the ratio 7:11 the volume of the cylinder is 13552cm3
​

Answer 1

Answer:

Let r,h be radius & hight of cylinder

⇒volume=πr

2

h,Total surface area (T.S.A)=2πr(h+r)

Given.

h

r

=

2

7

⇒h=

7

2r

Volume =πr

2

h=8316⇒πr

2

(

7

2r

)=8316

⇒r

3

=

2×22

8316×7×7

=

2×22

7

3

×1188

=7

3

×3

3

⇒r=7×3=21cm⇒h=

7

2

×21=6cm

T.S.A=2πr=(h+r)=2×

7

22

×21(6+21)=44×3×27

=3564cm

2

solution

Answer 2

Your Question :

The radius and the height of a cylinder are in the ratio 7:11, and the volume of the cylinder is 13552cm³.Find its radius of the base and its height.

Given Information :

• Radius and height of the cylinder are in the ratio 7:11.
• Volume of the cylinder is 13552 cm³.

To Find :

• Radius of the base.
• Height of the cylinder.

Solution :

Let the radius be r = 7x cm and the height be h = 11x cm.

Here, volume of the cylinder = 13552 cm³

$\sf{{ : \: ⟼ πr²h = 13552 cm³\: }{ \: }}$

$\sf{{ : \: ⟼ \: \frac{22}{7} × 7x × 7x × 11x = 13552\: }{ \: }}$

$\sf{{ : \: ⟼ \: 22 × 7 × 11x³ = 13552\: }{ \: }}$

$\sf{{ : \: ⟼ \: x³ = \frac{13552}{22 × 7 × 11} = 8\: }{ \: }}$

$\sf{{ : \: ⟼ x = 2\: }{ \: }}$

Therefore :

∴ The radius of the base is 7x cm = 14 cm and the height of the cylinder is 11x cm = 22cm.

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