Multiple choice

A cylinder of radius 3.5 cm and height 7 cm is melted to form two spheres such that radius of one is twice the radius of other. Find the volume of the smaller sphere.

  1. 22.76 cm3

  2. 29.94 cm3

  3. 32.5 cm3

  4. 43.9 cm3

  5. 35.64 cm3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Cylinder volume = pi * r^2 * h = pi * 3.5^2 * 7 = pi * 12.25 * 7 = 85.75 * pi = 269.39. Let radii be x and 2x. Sum of volumes = 4/3 * pi * x^3 + 4/3 * pi * (2x)^3 = 4/3 * pi * (x^3 + 8x^3) = 4/3 * pi * 9x^3 = 12 * pi * x^3. 12 * pi * x^3 = 85.75 * pi. x^3 = 85.75 / 12 = 7.1458. x = 1.926. Smaller sphere volume = 4/3 * pi * 1.926^3 = 4/3 * pi * 7.1458 = 29.94.

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