The amount of extra soap required to change the shape from a cone to a sphere is 1.5π.
What is the amount of extra soap needed?
Radius, r = 3 cm
Height, h = 1 cm
Volume of a cone = ⅓πr²h
= ⅓ × π × 3² × 1
= ⅓ × π × 9 × 1
= 3π
Diameter = 3 cm
Radius, r = diameter / 2
= 3/2
= 1.5 cm
Volume of a sphere = 4/3πr³
= 4/3 × π × 1.5³
= 4/3 × π × 3.375
= 4.5π
Therefore,
Amount of extra soap needed to change the shape = Volume of a sphere - Volume of a cone
= 4.5π - 3π
= 1.5π
Complete question:
A soap company changes the design of its soap from a cone to a sphere. The cone had a height of 1 cm and a radius of 3 cm. The sphere has a diameter of 3 cm. The amount of extra soap required to change the shape from a cone to a sphere is ______