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Surface Area Questions

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The Corbettmaths video tutorial on finding the surface area of a cuboid

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This section covers the order in which operations are carried out. The two main methods taught for working out the order of operations are BODMAS and BIDMAS.

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The Corbettmaths video tutorial on finding the Volume of a Cylinder

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Circle Song!

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Note that a measured length such as '12 cm to the nearest cm' means that the actual length lies between 11.5 cm and 12.5 cm.

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Volume & Surface Area

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Example 1

Calculate the volume of the cuboid shown.

Volume = 4 × 18 × 5 = 360 m³

Calculate the surface area of the cuboid shown.

Surface area

= (2 × 4 × 18) + (2 × 4 × 5) + (2 × 5 × 18)

= 144 + 40 + 180

= 364 m²

Example 2

Calculate the volume and total surface area of the cylinder shown.

Volume

=

π r² h = π × 4² × 6 = 96 π

Area of curved surface

=

2 π rh = 2 × π × 4 × 6

=

48 π

Area of each end

=

π r² = π × 4²

=

16 π

Note: From the working we can see that the area of the curved surface is 48 π, and that the area of each end is 16 π. The total surface area is therefore

48 π + (2 × 16 π)

= 80 π = 251.3274123 cm²

= 251 cm² (to 3 significant figures)

Example 3

Calculate the volume of this prism.

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Unit 9 Section 4 : Surface Area and Volume of 3-D Shapes

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Calculate the volume of the cuboid shown. Volume = 4 × 18 × 5 = 360 m³ Calculate the surface area of the cuboid shown. Surface area = (2 × 4 × 18) + (2 × 4 × 5) + (2 × 5 × 18) = 144 + 40 + 180 = 364 m² Calculate the volume and total surface area of the cylinder shown.

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Standard Form

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Standard form is a convenient way of writing very large or very small numbers. It is used on a scientific calculator when a number is too large or too small to be displayed on the screen.

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Unit 16 Section 4 : Formulae for circumference and area

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There are formulae to find the size of the area (A) and circumference (C) of a circle. To find either of these we need to use the size of the radius (r) or diameter (D).

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(b) Estimate the length of 29 pieces of wood layed end-to-end if each is 1.48m long. The actual calculation is 29 × 1.5. If we round the numbers to 1 significant figure we get 30 × 1. The In this case, we need to be sensible about the rounding, for example we could calculate 30 × 1.5.

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HCF & LCM

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Unit 2 Section 4 : Highest Common Factor and Lowest Common Multiple

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Although the methods above work well for small numbers, they are more difficult to follow with bigger numbers. Another way to find the highest common factor and lowest common multiple of a pair of numbers is to use the prime factorisations of the two numbers.