Question

Find the number of metallic circular discs with a 1.5 cm base diameter and of height  0.2 cm to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.

Answer 1

Given the diameter of the base of the the circular disc = 1.5 cm

Height = 0.2 cm

Volume of the circular disc =  \[\pi r^2 h = \pi\times\left( \frac{1 . 5}{2} \right)^2 \times 0 . 2 = \pi \times \left( 0 . 75 \right)^2 \times 0 . 2\]       ...(i)

Height of the cylinder = 10 cm

Diameter = 4.5 cm

Volume of the cylinder = 

\[\pi R^2 H = \pi \left( \frac{4 . 5}{2} \right)^2 \times 10 = \pi \times \left( 2 . 25 \right)^2 \times 10 . . . \left( ii \right)\]

Now since the circular discs are used to make the cylinder so, let n be the number of circular discs required.

\[n \times \text{ Volume of circular disc = Volume of cylinder}\]

\[\Rightarrow \frac{\text { Volume of cylinder } }{\text{ Volume of circular disc}} = n\]

\[\Rightarrow \frac{\pi \times \left( 2 . 25 \right)^2 \times 10}{\pi \times \left( 0 . 75 \right)^2 \times 0 . 2} = n\]

\[\Rightarrow n = 450\]

Hence, 450 metallic circular discs need to be melted to form the right circular cylinder.