Question

A hollow metallic cylinder whose external radius is 4.3 cm and internal radius is 1.1 cm and the whole length is 4 cm is melted and recast into a solid cylinder of 12 cm long. Find the diameter of a solid cylinder

Answer 1

External radius of the hollow cylinder R = 4.3 cm

Internal radius of the hollow cylinder r = 1.1 cm

Length of the cylinder (h) = 4 cm

Length of the solid cylinder (H) = 12 cm

Let the radius of the solid cylinder be x

Volume of the solid cylinder = Volume of the hollow cylinder

πr²H = πh(R² − r²)

x² × 12 = 4(4.3² − 1.1²)

12x² = 4 × 5.4 × 3.2

12x² = 4(4.3 + 1.1) (4.3 − 1.1)

x² = `(4 xx 5.4 xx 3.2)/12`

= `(4 xx 54 xx 32)/(12 xx 100)`

= `(54 xx 32)/(3 xx 100)`

= `(18 xx 32)/100`

x = `sqrt((18 xx 32)/100)`

= `sqrt((2 xx 9 xx 2 xx 16)/100)`

= `(2 xx 3 xx 4)/10`

= 2.4 cm

Diameter of the solid cylinder

= 2 × 2.4

= 4.8 cm