Perimeter, Area and Volume: Practice Set 3
Perimeter, Area and Volume: Practice Set 3 gives further practice with area, perimeter and volume, extending into working backwards from a given area or volume to find a missing length, finding the surface area of a cuboid, and multi-step problems that combine perimeter or area with cost or capacity. It follows the two earlier Perimeter, Area and Volume sets.
Before you start
Make sure you're comfortable with these topics first:
Method
- Identify whether the question wants a perimeter (a length), an area (a flat measurement) or a volume (a 3D measurement), since this decides which formula and which units to use.
- When you are given an area or volume and asked to find a missing length, rearrange the formula first, for example length = area / width for a rectangle, before substituting the numbers in.
- To find the surface area of a cuboid, work out the area of each of its three pairs of identical faces separately, then add up all six faces.
- For compound shapes and solids, split them into simpler rectangles, triangles or cuboids, calculate each part, and then add or subtract to find the total.
- Keep every measurement in the same unit throughout a multi-step calculation, converting at the start rather than partway through.
- State the correct unit for your final answer: length in cm or m, area in cm^2 or m^2, and volume in cm^3 or m^3.
Worked example
A cuboid has a volume of 240 cm^3. Its length is 8 cm and its width is 5 cm. Calculate its height.
- Write down the volume formula for a cuboid: volume = length x width x height.
- Rearrange to make height the subject: height = volume / (length x width).
- Substitute the given values: height = 240 / (8 x 5).
- Work out 8 x 5 = 40, then 240 / 40 = 6.
- The height of the cuboid is 6 cm.
Practice questions
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Q1A rectangle has an area of 72 cm^2 and a length of 9 cm. Find its width.Show answer
Answer: 8 cm (72 / 9)
Q2A cuboid has length 10 cm, width 4 cm and height 3 cm. Find its total surface area.Show answer
Answer: 164 cm^2 (2 x (40 + 30 + 12))
Q3A cuboid has a volume of 360 cm^3, a width of 6 cm and a height of 5 cm. Find its length.Show answer
Answer: 12 cm (360 / 30)
Q4A triangle has an area of 42 cm^2 and a base of 12 cm. Find its perpendicular height.Show answer
Answer: 7 cm (2 x 42 / 12)
Q5A rectangular swimming pool 20 m long and 8 m wide is surrounded by a path 2 m wide. Find the area of the path alone.Show answer
Answer: 128 m^2 (outer rectangle 24 m x 12 m = 288 m^2, minus the pool's 160 m^2)
Q6A cube has a volume of 125 cm^3. Find the length of one edge.Show answer
Answer: 5 cm (since 5 x 5 x 5 = 125)
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A rectangle has a perimeter of 42 cm and a width of 8 cm. Calculate its length.
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A cuboid-shaped water tank has a base measuring 1.2 m by 0.8 m and a height of 1.5 m. (a) Calculate the volume of the tank in cubic metres. (b) Given that 1 cubic metre holds 1000 litres, calculate the capacity of the tank in litres.
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A rectangular lawn measures 15 m by 10 m. A rectangular flower bed measuring 4 m by 3 m is dug out of one corner of the lawn. (a) Calculate the area of grass remaining. (b) The remaining grass is turfed at a cost of 6 pounds per square metre. Calculate the total cost of the turf.
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Free printable worksheet
Want more practice on paper? Download the perimeter, area and volume: practice set 3 worksheet pack - 13 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 28 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
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