3D shapes and volume：練習問題

A cube has a total surface area of \(150 \text{ cm}^2\). Calculate the length of one edge of the cube.

A solid cylinder has a radius of \(4\text{ cm}\) and a height of \(10\text{ cm}\). Calculate the volume of the cylinder. Give your answer to 3 significant figures.

A solid hemisphere has a total surface area of \(108\pi\text{ cm}^2\). Calculate the volume of the hemisphere, leaving your answer in terms of \(\pi\).

Calculate the volume of a sphere with a radius of \(3\text{ cm}\). Leave your answer in terms of \(\pi\).

A solid cylinder has a radius of \(3 \text{ cm}\) and a height of \(7 \text{ cm}\). Calculate the total surface area of the cylinder. Give your answer in terms of \(\pi\).

A prism has a cross-section area of \(15 \text{ cm}^2\) and a length of \(12 \text{ cm}\). Calculate the volume of the prism.

A solid metal sphere of radius \(3 \text{ cm}\) is melted down and recast into a solid cylinder with a radius of \(2 \text{ cm}\). Calculate the vertical height of the cylinder.

A sphere has a surface area of \(144\pi \text{ cm}^2\). Calculate the volume of the sphere, leaving your answer in terms of \(\pi\).

The diagram shows a triangular prism. The cross-section is a right-angled triangle with a base of \(6 \text{ cm}\) and a height of \(8 \text{ cm}\). The length of the prism is \(15 \text{ cm}\).

(a) Calculate the volume of the prism.
(b) Calculate the total surface area of the prism.

A hollow metal cylinder has an external radius of \(7 \text{ cm}\), an internal radius of \(4 \text{ cm}\) and a height of \(15 \text{ cm}\).

(a) Calculate the volume of the metal used to make the cylinder. Give your answer to 1 decimal place.
(b) The density of the metal is \(8.5 \text{ g/cm}^3\). Calculate the mass of the cylinder. Give your answer in kilograms to 2 decimal places.