Surface area and volume：練習問題

A cylinder and a cone both have the same radius \(r = 6\) cm and the same height \(h = 10\) cm. Calculate the difference in their volumes, giving your answer in terms of \(\pi\).

A composite solid toy is formed by joining a hemisphere of radius 3 cm to the base of a cone with the same radius and a slant height of 5 cm. Calculate the total surface area of the toy in terms of \(\pi\).

A sphere has a radius of 3 cm. Calculate the volume of the sphere in terms of \(\pi\).

Calculate the volume of a cylinder with a radius of 4 cm and a height of 10 cm. Give your answer in terms of \(\pi\).

Calculate the total surface area of a solid hemisphere with a radius of \(6\text{ cm}\). Give your answer in terms of \(\pi\).

A storage container is made of a hollow cylinder with a hemispherical base. The cylinder has a radius of 6 cm and a height of 10 cm.

(a) Calculate the total volume of the container. Leave your answer in terms of \(\pi\).
(b) The external surface of the container (excluding the open top) is to be painted. Calculate the total surface area to be painted in terms of \(\pi\).
(c) If the container is filled with water to \(75\%\) of its total volume, calculate the depth of the water from the lowest point of the hemisphere. Round your answer to 3 significant figures.