Four times the area of the curved surface of a cylinder is equal to 6

1.	Four times the area of the curved surface of a cylinder is equal to 6 times the sum of the areas of its bases. If its height is 12 cm. then its volumes, in cm3 is1. 48π2. 384π3. 546π4. 768π
Answer» Correct Answer - Option 4 : 768π Given: 4 (A) = 6 (B) h = 12 cm Where, A = Area of CSA of cylinder B = Sum of the area of its base h = height of cylinder Formula used: Curved surface area of cylinder = 2π × radius × height Volume of cylinder = π × (radius)2 × height Area of base = π × (radius)2 Calculation: 4 (A) = 6 (B) ⇒4 (2 π r h) = 6 (2 π r²) ⇒ 8 h = 12 r ⇒ 8 × 12 = 12 r (given h= 12 cm) ⇒ r = 8 cm Volume of cylinder = π × 8² × 12 = 768 π

Four times the area of the curved surface of a cylinder is equal to 6 times the sum of the areas of its bases. If its height is 12 cm. then its volumes, in cm3 is1. 48π2. 384π3. 546π4. 768π

Answer» Correct Answer - Option 4 : 768π

Given:

4 (A) = 6 (B)

h = 12 cm

Where,

A = Area of CSA of cylinder

B = Sum of the area of its base

h = height of cylinder

Formula used:

Curved surface area of cylinder = 2π × radius × height

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

Area of base = π × (radius)2

Calculation:

4 (A) = 6 (B)

⇒4 (2 π r h) = 6 (2 π r²)

⇒ 8 h = 12 r

⇒ 8 × 12 = 12 r (given h= 12 cm)

⇒ r = 8 cm

Volume of cylinder = π × 8² × 12

= 768 π

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Four times the area of the curved surface of a cylinder is equal to 6 times the sum of the areas of its bases. If its height is 12 cm. then its volumes, in cm3 is1. 48π2. 384π3. 546π4. 768π

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