# StudySquare

# 3D shapes for OCR GCSE Maths

This page covers the following topics:

1. Cubes and cuboids

2. Prisms

3. Cylinders

4. Pyramids

5. Cones and spheres

A cube is a 3D-shape made up of six squares, three of which meet at each vertex. A cuboid is a 3D-shape made up of six rectangles, three of which meet at each vertex. Opposite faces on a cuboid are equal. The surface area of cubes and cuboids can be found by adding the areas of the individual faces. The volume of both cubes and cuboids can be found using the following formula: V = length × width × height.

A prism is a 3D-shape whose cross section is the same shape throughout its length. The volume of a prism is calculated by finding the cross-sectional area and multiplying it by its length.

A cylinder is a 3D-shape with a circular cross-setion and a curved surface. Its volume can be calculated by multiplying the cross-sectional area, ie. the area of the circle, with its height. The surface area can be calculated by adding the areas of the two circles and the area of the curved surface. The area of the curved surface can be found by imagining it as an open rectangle, whose length is equal to the circumference of the circle.

A pyramid is a 3D-shape with a polygon base and triangular sides which meet at the top of the shape. The volume of a pyramid can be calculated using the following formula: Volume = 1/3 × base area × perpendicular height. The surface area of a pyramid can be calculated by adding the areas of the faces.

A sphere is a 3D-shape that is the surface of a ball. It is formed by rotating a circle about its diameter. The set of all points on a sphere are all at the same distance from the centre of the sphere. The distance is known as the radius of the sphere. The volume of a sphere is calculated using the following formula: V = 4/3 × πr³. The surface area of a sphere is calculated using the following formula: Surface area = 4πr². A cone is a 3D-shape with a circular base around which it tapers smoothly. A cone is a third of a cylinder of the same height and diameter, therefore its volume is given by the following formula: V = 1/3 × πr²h. The curved surface area of a cone is given by: πrl, and thus its total surface area is the sum of this and the area of the base circle.

# 1

State how many faces a cube has.

A cube has 6 faces.

# 2

State how many faces a cuboid has.

A cuboid has 6 faces.

# 3

A pyramid is made up of a square base with side 4 cm and has perpendicular height 7 cm. Calculate the volume of the pyramid.

Volume = 1/3 × (4)(4) × 7 = 37.3 cm³ (to 3 significant figures).

# 4

How can the surface area of a pyramid be calculated?

The surface area of a pyramid can be calculated by adding the areas of the faces.

# 5

What can be said about opposite faces of a cuboid?

Opposite faces of a cuboid are equal.

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