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Maths

3D shapes - Higher

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Volume and surface area

Pyramid

A pyramid is any shape that goes up to a point at the top. The base can be any shape, but when the base is a circle it is called a cone.

image: pyramid

The volume of a pyramid is:

1/3 × base area × perpendicular height

The surface area of a pyramid is the area of the base + the area of all the other sides.

Cone

image: cone

The volume of a cone is:

1/3πr2h

The curved surface area of a cone is:

πrL

(where L is the slant height).

Note this doesn't include the area of the base, which is a circle, area πr2.

Frustum

image: frustrum

The frustum of a cone is the shape left when its top has been cut off.

To calculate the volume of a frustum, find the volume of the original cone, find the volume of the smaller, missing cone, and subtract.

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