Question

Lateral surface Area of a cylinder is 94.2 cm² its height is 5 cm .Find :-

i) Radius of the base .
ii) Its volume (Use $\pi$ = 3.14 )


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Answer 1

2πrh = 94.2

3.14×r×5=47.1

$5r = \frac{47.10}{3.14}$

5r=15

r=3

v =πr²h =3.14×3²×5 = 141.3cm³

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Answer 2

Given

• LSA of Cylinder = 94.2cm².
• Height = 5cm.
• Value of π = 3.14.

To Find

• Radius of the base.
• Volume of Cylinder.

Formula to be Used

• LSA of Cylinder = 2πrh.
• Volume of Cylinder = πr²h.

Solution

Calculating Radius of the Base

LSA of Cylinder = 94.2cm

Height = 5cm.

By formula of LSA, we have

LSA of Cylinder = 2 πrh

⇒ 94.2 = 2 × 3.14 × r × 5

⇒ 94.2 = 31.4r

⇒ r = 94.2/31.4

⇒ r = 3 cm.

Therefore, radius of base is 3 cm.

Verification

Height = 5cm.

Radius = 3cm.

LSA of Cylinder = 2 πrh

⇒ LSA of Cylinder = 2 × 3.14 × 3 × 5

⇒ LSA of Cylinder = 94.2 cm.

We can see that we got LSA of Cylinder from Radius and Height, hence our answer is correct!

Answer verified!

Calculating Volume of Cylinder

Height = 5cm.

Radius = 3cm.

Volume of Cylinder = πr²h

⇒ Volume of Cylinder = 3.14 × (3)² × 5

⇒ Volume of Cylinder = 3.14 × 9 × 5

⇒ Volume of Cylinder = 141.3 cm³.

Therefore, volume of cylinder is 141.3 cm³.

Verification

Volume of Cylinder = 141.3 cm³.

Height = 5 cm.

By formula of volume of cylinder, we have

Volume of Cylinder = πr²h

⇒ 141.3 = 3.14 × r² × 5

⇒ 141.3 = 15.7r²

⇒ r² = 141.3/15.7

⇒ r² = 9

⇒ r = √9

⇒ r = 3 cm.

We can see that we got radius from height and volume of cylinder, hence our answer is correct!

Answer verified!

Final Answer

• Radius of base = 3 cm.
• LSA of Cylinder = 141.3 cm³.

Used Abbreviations

• LSA = Lateral Surface Area.
• r = Radius.
• h = Height.

Related Formulas

• Volume of Cuboid = lbh.
• Volume of Cube = a³.
• Volume of Hollow Cylinder of External and Internal Radius = πR²h - πr²h.
• SA of Cube = 6a².
• SA of Cuboid = 2(lb + bh + hl).
• TSA of Cylinder = 2πr(r + h).

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