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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?

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? Correct Answer 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

⇒ 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.

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