Surface Areas and Volumes · Class 10 · CBSE Mathematics

How many solid spherical bullets, each of diameter 4 text{ cm}, can be made out of a solid rectangular lead block of dimensions 22 text{ cm} times 12…

Practice question from Surface Areas and Volumes (Class 10 · CBSE Mathematics), with the correct answer and a step-by-step solution.

medium · MCQ · Q-AF0CA9

How many solid spherical bullets, each of diameter 4 cm4 \text{ cm}, can be made out of a solid rectangular lead block of dimensions 22 cm×12 cm×5 cm22 \text{ cm} \times 12 \text{ cm} \times 5 \text{ cm}? (Take π=227\pi = \frac{22}{7})

  1. A.315Correct answer
  2. B.312.5
  3. C.310
  4. D.320

Solution

Volume of rectangular block = 22×12×5=1320 cm322 \times 12 \times 5 = 1320 \text{ cm}^3. Radius of each spherical bullet = 2 cm2 \text{ cm}. Volume of one bullet = 43×227×(2)3=70421 cm3\frac{4}{3} \times \frac{22}{7} \times (2)^3 = \frac{704}{21} \text{ cm}^3. Number of bullets = Volume of blockVolume of one bullet=1320×21704=315\frac{\text{Volume of block}}{\text{Volume of one bullet}} = \frac{1320 \times 21}{704} = 315.

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