Question

Radius of a solid copper cylinder is 4.2 cm and its height is 16 cm. How many discs of diameter 1.4 cm and thickness 0.2 cm can be made from this cylinder melting it.

Answer 1

radius of solid copper cylinder , R = 4.2 cm
height of solid copper cylinder , H = 16 cm
so, volume of solid copper cylinder = πR²H
= 22/7 × 4.2 × 16
= 22 × 0.6 × 16
= 22 × 9.6
= 211.2 cm²

thickness of disc , h = 0.2 cm
radius of disc , r = diameter/2 = 1.4/2 = 0.7 cm
now, volume of disc = πr²h
= 22/7 × 0.7 × 0.2
= 22 × 0.1 × 0.2
= 0.44 cm²

$\textbf{\underline{number of discs}}=\frac{\text{volume of cylindrical copper solid}}{\text{volume of each disc}}$

= 211.2/0.44 = 480

hence, number of discs = 480

Answer 2

Radius of a solid copper cylinder = 4.2 cm and

Height of the solid copper cylinder = 16 cm.

Volume of the cylinder = pi x r x r x h = 3.14 x 4.2 x 4.2 x 16 = 886.23 cbcm.

Volume of one disc of diameter 1.4 cm and thickness 0.2 cm = 3.14 x 0.7 x 0.7 x 0.2 = 0.307cbcm.

Therefore, number of discs of diameter 1.4 cm and thickness 0.2 cm that can be made from this cylinder melting it = 886.23 cbcm / 0.307cbcm = 2886.7 approxly 2886 discs. (Ans)