Question

A metallic sphere is immersed in water in a cylindrical container causing a rise in the level of water by 7.5cm if the cylinder has a base radius of 7cm find the radius of the sphere to 2 decimal places

Answer 1

Answer:

6.51 cm

Step-by-step explanation:

Since the sphere causes the water level in the cylindrical container to rise and thus increase by its own volume, the volume of the sphere is V = 4πr³/3 where r = radius of sphere. The volume rise of the container is thus    V' = πR²h where R = radius of base of cylinder = 7 cm and h = height of water level = 7.5 cm.

Since V = V',

4πr³/3 = πR²h

dividing through by π, we have

4r³/3 = R²h

multiplying both sides by 3/4, we have

r³ = 3R²h/4

taking cube-root of both sides, we have

r = ∛(3R²h/4)

Substituting the values of the variables into the equation, we have

r = ∛(3(7 cm)² × 7.5 cm/4)

r = ∛(3 × 49 cm² × 7.5 cm/4)

r = ∛(1102.5cm³/4)

r = ∛(275.625 cm³)

r = 6.508 cm

r ≅ 6.51 cm to 2 decimal places