The Ratio between Curved surface area and Total Surface area of a cyli

1.	The Ratio between Curved surface area and Total Surface area of a cylinder is 7 : 11. If Curved surface area is 704 cm2 then find the volume of the cylinder.1. 2434 cm32. 2832 cm33. 2816 cm34. 2756 cm3
Answer» Correct Answer - Option 3 : 2816 cm³ Given: Ratio of Curved surface and total surface area of cylinder = 7 : 11 Curved surface area of cylinder = 704 cm² Formula Used: Curved surface area = 2πrh , where r = radius of base and h = height of cylinder Total Surface area = 2πrh + 2πr² = 2πr(h + r) Volume of cylinder = πr²h Calculation: (2πrh)/[2πr(h + r)] = 7/11 ⇒ h/(h + r) = 7/11 ⇒ 11h = 7h + 7r ⇒ 4h = 7r ⇒ h/r = 7/4 Let the height be 7x and radius be 4x, then, 704 = 2 × (22/7) × 7x × 4x ⇒ x² = (704 × 7)/(28 × 22 × 2) ⇒ x² = 4 ⇒ x = 2 Putting values back in 7x and 4x we get, Radius = 4x = 4 × 2 = 8 cm Height = 7x = 7 × 2 = 14 cm Volume of cylinder = (22/7) × 8 × 8 × 14 ⇒ V = 2816 cm³ ∴ The volume of cylinder is 2816 cm³.

The Ratio between Curved surface area and Total Surface area of a cylinder is 7 : 11. If Curved surface area is 704 cm2 then find the volume of the cylinder.1. 2434 cm32. 2832 cm33. 2816 cm34. 2756 cm3

Answer» Correct Answer - Option 3 : 2816 cm³

Given:

Ratio of Curved surface and total surface area of cylinder = 7 : 11

Curved surface area of cylinder = 704 cm²

Formula Used:

Curved surface area = 2πrh , where r = radius of base and h = height of cylinder

Total Surface area = 2πrh + 2πr² = 2πr(h + r)

Volume of cylinder = πr²h

Calculation:

(2πrh)/[2πr(h + r)] = 7/11

⇒ h/(h + r) = 7/11

⇒ 11h = 7h + 7r

⇒ 4h = 7r

⇒ h/r = 7/4

Let the height be 7x and radius be 4x, then,

704 = 2 × (22/7) × 7x × 4x

⇒ x² = (704 × 7)/(28 × 22 × 2)

⇒ x² = 4

⇒ x = 2

Putting values back in 7x and 4x we get,

Radius = 4x = 4 × 2 = 8 cm

Height = 7x = 7 × 2 = 14 cm

Volume of cylinder = (22/7) × 8 × 8 × 14

⇒ V = 2816 cm³

∴ The volume of cylinder is 2816 cm³.