Question

find the volume of a cylinder in litres whose curved surface area is 154m² and height is 3.5​

Answer 1

Answer

Volume of the cylinder is 539m³

Explanation:

Given

• Curved surface area of the cylinder = 154 m²
• Height of the cylinder = 3.5 m

To Find

• Volume of the cylinder.

Solution

Curved surface area = 2π × radius × height

➡ 154m² = 2πr × 3.5 m

➡ 154m²/2 = πr × 3.5 m

➡ 77m² = πr × 3.5 m

➡ 77m²/3.5m = πr

➡ 22m = πr

➡ 22m = 22/7 × r

➡ 22m × 7/22 = r

➡ 7m = r

Radius of the cylinder is 7 m

Volume of a cylinder = π (radius)² × height

Volume = π ( 7m )² × 3.5 m

Volume = π × 49m² × 3.5m

Volume = π × 171.5 m³

Volume = 22/7 × 171.5 m³

Volume = 539m³

Volume of the cylinder is 539m³

Answer 2

$\large\underline{\underline{\sf{\maltese\:\: \red{Correct \: Question \: : }}}}$

Find the volume of a cylinder in litres whose curved surface area is 154m² and height is 3.5m.

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$\large\underline{\underline{\sf{\maltese\:\: \red{Answer \: : }}}}$

Volume of cylinder (V) in litres = $\boxed{\bold{ \underline{539000 \: Liters}}}$.

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$\large\underline{\underline{\sf{\maltese\:\: \blue{Given \: :}}}}$

• Curved Surface Area (CSA) of cylinder = 154m²

• Height of cylinder (h) = 3.5 m

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$\large\underline{\underline{\sf{\maltese\:\: \blue{To \: Find \: :}}}}$

• Volume of cylinder (V) in litres = ?

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$\large\underline{\underline{\sf{\maltese\:\: \blue{Concepts \: Implented \: :}}}}$

• Curved Surface Area of cylinder (CSA) = 2πrh

• Volume of cylinder (V) = πr²h

• 1 m³ = 1000 Litres

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$\large\underline{\underline{\sf{\maltese\:\: \blue{Solution \: :}}}}$

$\sf Curved \: Surface \: Area \: (CSA) \: of \: cylinder = 154m^2$

$\implies \sf 2\pi rh = 154m^2$

$\sf\implies 2 \times \frac{22}{7} \times r \times 3.5m = 154 m^2$

$\sf \implies r = \dfrac{154m^2 \: \times \: 7}{2 \: \times \: 22 \: \times \: 3.5m}$

$\sf\implies r = \bold{7m}$

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$\sf Volume \: of \: cylinder (V) = \pi r^2h$

$\implies \sf V = \frac {22}{7} \: \times \: 7m \: \times \: 7m \: \times \: 3.5m$

$\implies \sf V = \bold{539 m^3}$

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1m³ = 1000 L

539m³ = 539 × 1000 L

539m³ = 539000 L

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∴ Volume of cylinder (V) in litres = $\boxed{\bold{ \underline{539000 \: Liters}}}$.

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