Question

Find the number of coins of 1.5 cm diameter and 0.2 cm thickness to be melted to form a right circular cylinder of height 5 cm and diameter 4.5 cm.

Answer 1

Formula used :

$\boxed{\mathbf{Volume \: of \: Cylinder = π{r}^{2}h}}$

Given,

The diameter of coin = 1.5cm.
Radius = 1.5/2 cm which can also be written as 15/20 cm.
Thickness of the coin (height) = 0.2cm = 2/10 cm

Diameter of the reshaped cylinder = 4.5cm.
Radius = 4.5/2 cm = 45/20 cm.
Height = 5cm.

$\underline{\underline{\huge\mathfrak{Solution}}}$

Let the number of coins be x.


The Volume of coins × x = Volume of reshaped Cylinder.

$\pi \times \frac{15}{20} \times \frac{15}{20} \times \frac{2}{10} \times x= \pi \times \frac{45}{20} \times \frac{45}{20} \times 5 \\ \\ \frac{3}{4} \times \frac{3}{4} \times \frac{1}{5} \times x = \frac{9}{4} \times \frac{9}{4} \times 5 \\ \\ x = \frac{9}{4} \times \frac{9}{4} \times 5 \times \frac{1}{5} \times \frac{4}{3} \times \frac{4}{3} \\ \\ x = 9$

$\bf \therefore 9 \: coins \: are \: to \: be \: melted \: to \: form \\ \bf a \: cylinder \: with \: given \: measures$