Answer:
a. 452.4 cm³ to the nearest tenth b. 113.1 cm³ to the nearest tenth
c. 5.0 cm to the nearest tenth
Explanation:
a. The volume of the water V₁ = πr²h since it is in a cylindrical container. r = 6 cm and h = 10 cm - 6 cm = 4 cm (since it is filled to a depth of 6 cm measuring from the top, so we have a height from the bottom of 10 cm - 6 cm = 4 cm).
So, V₁ = πr²h
= π × (6 cm)² × 4 cm
= 452.39 cm³
= 452.4 cm³ to the nearest tenth
b. The volume of the sphere V₂ = 4πr³/3 where r = radius of sphere = 3 cm.
V₂ = 4πr³/3
= 4π(3 cm)³/3
= 113.1 cm³ to the nearest tenth
c. When the sphere is placed in the container, the new volume of water in the container would be V = V₁ + V₂
So V = 452.4 cm³ + 113.1 cm³ = 565.5 cm³
Since the volume of water is still the volume of a cylinder, its height h is
h = V/πr²
= 565.5 cm³/π(6 cm)²
= 5.0 cm to the nearest tenth