Question

The sum of the outer and inner curved surface areas of a cylinder 14 cm long is 352 cm². Find the outer and the inner radii of the cylinder if the volume of the metal is 176 cm².

Answer 1

Given:

Height of cylinder,
h = 14cm

Sum of outer and inner curved surface areas,

2πRh + 2πrh = 352 cm²

Volume of metal

πh(R² − r²) = 176 cm³

Let outer radius = R, inner radius = r

Step 1: Use sum of curved surface areas

2πh(R + r) = 352

Substitute h = 14 π = `22/7`

`2 xx 22/7 xx 14(R + r) = 352`

88 (R + r) = 352

R + r = 4               ...(1)

Step 2: Use the volume of metal

πh(R2 − r2) = 176

`22/7 xx 14(R^2 − r^2) = 176`

44(R² − r²) = 176

R² − r² = 4

(R − r) (R + r) = 4

(R − r) × 4 = 4 ⇒ R − r = 1        ...(2)

Step 3: 

R + r = 4

R − r = 1

2R = 5 ⇒ R = 2.5 cm

r = 4 − 2.5 = 1.5 cm