Question

A cylinder is filled up with water to 3 4 its total capacity. The solid sphere is dropped completely into the cylinder. How high up the container will the water reach after the sphere is fully submerged? Give your answer rounded to 1 DP.

Answer 1

30.3 cm

Explanation:

Suppose the height is h after the sphere is full submerged.

4/3
`\pi`R³ =
`\pi`r²(h-30) The volume of the sphere is equal to the volume

4/3
`\pi x`(10/2)³=
`\pi` × (14/2)²(h-30) of the water surface rising

4/3 × 125 = 49 × (h-30)

h - 30 = 49 × 3/4 × 125

h - 30 = 0.3

h = 30 + 0.3

h = 30.3 cm