Surface Area and Volume

10 Maths: Chapter 4

Outline of Unit

By the end of this unit you should be able to calculate:

  1. Surface area of a prism
  2. Surface area of a cylinder
  3. Surface area of a pyramid*
  4. Surface area of cones and spheres*
  5. Surface areas of composite solids
  6. Volumes of prisms and cylinders
  7. Volumes of pyramids, cones and spheres*
  8. Volumes of composite solids*
  9. Areas of similar figures*
  10. Surface areas and volumes of similar solids*

Items marked with an * are 5.03 work.

1. Surface area of a prism

The surface area of a solid is the total area of all the faces of the solid. To calculate the surface area of a solid find the area of each face and add all the areas together.

You need to know the follow formulae:

  • Area of a square/rectangle
  • Area of a circle
  • Area of a parallelogram/rhombus
  • Area of a trapezium
  • Pythagoras' Theorem

2. Surface area of a cylinder

The surface area of a closed cylinder is:
Surface area = area of two circles + area of a rectangle
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how to find the surface area of a cylinder

3. Surface area of a pyramid

A pyramid is a solid shape with a polygon (usually a rectangle, square, or triangle) for the base and triangular faces that meet at a point called the apex.

The video below explains how to calculate the surface area of a pyramid

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Surface Area Of A Pyramid

4. Surface areas of cones and spheres

To calculate the surface area of cones and spheres use the formulae below
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Surface Area Of A Cone - VividMaths.com

5. Surface area of composite solids

Is calculated by adding together the smaller areas. Formulae you need to know include:

  • Rectangle/square
  • Triangle
  • Circle (+ semi circle)/sphere
  • Trapezium
  • Parallelogram/rhombus

Surface Area of Three Dimensional Figures, Composite Solids, and Missing Dimensions

6. Volumes of prisms and cylinders

The volume of a solid is the amount of space it occupies.

Volume is measured in cubic units, e.g. cubic metres or cubic centimetres.

The main formula you need to know are the formula for volume of a prism, and also volume of a cylinder. Volume of a cylinder is just an application of volume of a prism

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Find the volume of a triangular prism and cube | Geometry | Khan Academy

Capacity

The capacity of a container is how much liquid or gas it can hold.

Capacity is measured in millilitres (mL), litres (L), kilolitres (kL - 1000L), and megalitres (mL 1,000,000L)

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7. Volume of pyramids, cones, and spheres

The volume of a cone and a pyramid can be found by multiplying the area of the base by the perpendicular height of the pyramid/cone.

The volume of a sphere is slightly different

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Volume of a cone | Perimeter, area, and volume | Geometry | Khan Academy
Volume of a sphere | Perimeter, area, and volume | Geometry | Khan Academy

8. Volumes of composite solids

The formula you need to know are below.

Note: surface area is in two dimensions and the units are squared

Volume is three dimensions and the units are cubed

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Volume Of Composite Figures