Multiple choice

The number of coins of radius $0.75 cm$ and thickness $0.2 cm$ are to be melted to make a right circular cylinder of height $8 cm$ and base radius $3 cm$ is

  1. $460$
  2. $500$
  3. $600$
  4. $640$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of cylinder = pi * 3^2 * 8 = 72 * pi. Volume of one coin = pi * 0.75^2 * 0.2 = pi * 0.5625 * 0.2 = 0.1125 * pi. Number of coins = 72 / 0.1125 = 640.

AI explanation

The volume of the newly formed cylinder must equal the combined volume of all the melted coins, so we divide the volume of the large cylinder by the volume of a single coin to find the number. The large cylinder has a volume of pi times 3 squared times 8, which equals 72 pi. Each coin is a small cylinder with volume pi times 0.75 squared times 0.2, which simplifies to 0.1125 pi. Dividing 72 pi by 0.1125 pi results in exactly 640 coins.

Keep practicing — related questions