Multiple choice

A cylindrical vessel of radius 7 cm is partially filled with water. By how much will the water level rise, if a sphere of radius 6 cm is completely immersed in this water?

  1. 11.76 cm

  2. 17.64 cm

  3. 23.52 cm

  4. 5.88 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of sphere = (4/3) * pi * 6^3 = 288 * pi. Volume of displaced water in cylinder = pi * r^2 * h = pi * 7^2 * h = 49 * pi * h. Equating them: 49 * h = 288, so h = 288/49 = 5.877 cm.

AI explanation

When the sphere is submerged, the volume of the displaced water equals the volume of the sphere, which causes the water level in the cylinder to rise. The volume of the sphere is 4 thirds pi times the radius 6 cubed, resulting in a volume of 288 pi cubic centimeters. This volume is spread across the base of the cylindrical vessel, which has an area of pi times 7 squared, or 49 pi square centimeters. Dividing the sphere volume by the cylinder base area gives 288 pi divided by 49 pi, so the water level rises by approximately 5.88 centimeters.

Keep practicing — related questions