Surface area and volume：練習問題

A pyramid has a square base with a side length of 6 cm and a vertical height of 5 cm. Calculate the volume of the pyramid.

In the diagram, a prism has a cross-section in the shape of a right-angled triangle with base 4 cm and height 3 cm. The length of the prism is 10 cm. Calculate its volume.

A solid object is made from a cylinder with radius \(5\) cm and height \(12\) cm, and a cone placed on top of it. The cone has the same radius as the cylinder and a slant height of \(13\) cm. Calculate the total surface area of the solid object. Give your answer in terms of \(\pi\).

A cone has a radius of 3 cm and a vertical height of 4 cm. Calculate the volume of the cone, leaving your answer in terms of \(\pi\).

The diagram shows a cone with radius 5 cm and slant height 13 cm. Calculate the total surface area of the cone in terms of \(\pi\).

Calculate the volume of a sphere with a radius of \(3\) cm. Give your answer in terms of \(\pi\).

A solid cylinder has a volume of \(400\pi\) cm³ and a height of \(16\) cm. Calculate the curved surface area of the cylinder, leaving your answer in terms of \(\pi\).

A solid metal cuboid measuring \(12 \text{ cm}\) by \(10 \text{ cm}\) by \(5 \text{ cm}\) is melted down and recast into a solid cylinder of radius \(4 \text{ cm}\). Calculate the height of the cylinder to 3 significant figures.

A rectangular prism (cuboid) has a length of 8 cm, a width of 5 cm, and a height of 10 cm.

(a) Calculate the volume of the prism.

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

(c) If the cuboid is made of a material with a density of \(2.5 \text{ g/cm}^3\), calculate its mass in kilograms.

A solid sphere of radius 6 cm is melted down and all the metal is used to cast identical solid cones. Each cone has a radius of 3 cm and a height of 5 cm.

(a) Calculate the volume of the sphere.

(b) Calculate the volume of one cone.

(c) Determine the maximum number of such cones that can be cast from the metal of the sphere.

(d) If 10% of the metal is wasted during the melting and casting process, how many cones can now be cast? Give your answer as a whole number.