Question

A hollow cylinder of height 3 cm is melted and cast into a solid cylinder of height 9 cm. If the outer radius and inner radius of the hollow cylinder are 4.3 cm and 1.1 cm, respectively, then what is the total surface area (in cm²) of the solid cylinder?
1. 54.72 π
2. 48.96 π
3. 57.12 π
4. 50.36 π

Answer 1

Correct Answer - Option 1 : 54.72 π

Given:

A hollow cylinder of height 3 cm is melted and cast into a solid cylinder of height 9 cm

he outer radius and inner radius of the hollow cylinder are 4.3 cm and 1.1 cm

Formula used:

Volume of solid cylinder = πr2h

Volume of hollow cylinder = πR²h - πr²h = πh(R² - r²)

Total surface area = 2πr(h + r)

Calculation:

let the solid cylinder radius be x.

Volume of hollow cylinder = πh(R2 - r2)

⇒ π3[(4.3)2 - (1.1)2]

⇒ π3(5.4 × 3.2)      ----(1)

Volume of solid cylinder = πx²9    ----(2)

From equation(1) and equation(2);

π3(5.4 × 3.2) = πx29

⇒ x² = (18 × 32)/100 = 576/100

⇒ x2 = (24/10)²

⇒ x = 2.4

Total surface area = 2πr(h + r)

⇒ 2 × π × 2.4(2.4 + 9)

⇒ 2 × π × 2.4 × 11.4

⇒ 54.72 π cm²

∴ The total surface area (in cm2) of the solid cylinder is 54.72 π cm2.