Multiple choice

Twelve solid hemispheres of the same size are melted and recast to a right circular cylinder of diameter 7 cm and height 28 cm. What is the radius of the hemispheres?

  1. 4.5 cm

  2. 3.5 cm

  3. 3 cm

  4. 3.8 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of 12 hemispheres = 12 * (2/3) * pi * r^3 = 8 * pi * r^3. Volume of cylinder = pi * (3.5)^2 * 28 = pi * 12.25 * 28 = 343 * pi. 8 * r^3 = 343, r^3 = 343/8, r = 7/2 = 3.5.

AI explanation

Using the volume conservation method, the volume of the twelve hemispheres equals the volume of the newly formed cylinder. The volume of each hemisphere is (2/3) times pi times r cubed, and the volume of the cylinder is pi times R squared times height, which is pi times 3.5 squared times 28. Equating 12 times (2/3) times pi times r cubed to pi times 12.25 times 28 gives r cubed equal to 42.875. Taking the cube root, the radius of each hemisphere is 3.5 cm.

Keep practicing — related questions