Multiple choice

A hemisphere of radius 6 cm is cast into a right circular cone of height 75 cm. What is the radius of the base of the cone?

  1. 2.4 cm

  2. 1.6 cm

  3. 2.6 cm

  4. 4.2 cm

  5. 4.3 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of hemisphere = (2/3) * pi * r^3 = (2/3) * pi * 6^3 = 144 * pi. Volume of cone = (1/3) * pi * R^2 * h = (1/3) * pi * R^2 * 75 = 25 * pi * R^2. Equating volumes: 144 * pi = 25 * pi * R^2. R^2 = 144/25 = 5.76. R = 2.4 cm.

AI explanation

By the volume conservation method, the volume of the hemisphere equals the volume of the right circular cone. Using the formulas, (2/3) times pi times 6 cubed equals (1/3) times pi times r squared times 75. Canceling pi from both sides gives 144 equal to 25 times r squared. Solving for r gives a base radius of 2.4 cm.

Keep practicing — related questions