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Find the number of coins, 2.5 cm in diameter and 0.4 cm thick, to be melted to form a right circular cylinder of height 15 cm and diameter 8 cm.

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324

372

368

384

answer is D.

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Detailed Solution

Here, the radius of the coin=

\frac{diameter}{2} = \frac{2.5}{2} = 1.25 cm

Now we know that coins are of cylindrical shape so their volume will be given by the formula π

r^{2} h

where r is radius and h is height of the coin,
So we get the volume of the coin as,
=

π \times {(1.25)}^{2} \times 0.4 = π {(1.25)}^{2} \times 0.4

Now, Volume of n number of coins =n

π {(1.25)}^{2} \times 0.4

first radius of the cylinder is given as =

\frac{diameter}{2} = \frac{8}{2} = 4 cm

Hence volume of cylinder we get as, π

r^{2} h = π \times 4^{2} \times (15)

Now equation the volume of the cylinder with the volume of n number of coins, we get
Or, n

π {(1.25)}^{2} \times 0.4 = π \times 4^{2} \times (15)

Or,n=

\frac{4^{2} \times (15)}{{(1.25)}^{2} \times 0.4} = 384

Hence, we get the number of coins as 384.
Hence, option 4 is correct.

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