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Grade 4 · Foundation and Higher · free GCSE maths worksheet

Surface area of cuboids and prisms

Adding the areas of every face.

14 original questions, 53 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

A cube has sides of length 4 cm.

Work out the total surface area of the cube.

2 marks
Show answer
96 cm2
2

A cuboid measures 5 cm by 3 cm by 2 cm.

Work out the total surface area of the cuboid.

State the units of your answer.

3 marks
Show answer
62 cm²
3

A cube has a volume of 64 cm3.

Work out the total surface area of the cube.

3 marks
Show answer
96 cm²
4

A fish tank is a cuboid with no lid. It is 80 cm long, 50 cm wide and 40 cm high.

Work out the area of glass needed to make the tank.

3 marks
Show answer
14400 cm2
5

A prism has a right-angled triangle as its cross-section. The triangle has sides of length 3 cm, 4 cm and 5 cm. The prism is 10 cm long.

Work out the total surface area of the prism.

4 marks
Show answer
132 cm2
6

The cross-section of a triangular prism is a right-angled triangle with base 3 cm, height 4 cm and hypotenuse 5 cm.

The length of the prism is 10 cm.

Work out the total surface area of the prism.

3 cm4 cm10 cm5 cm
3 marks
Show answer
132 cm²
7

A solid is made by placing a cube of side 4 cm centrally on top of a cuboid.

The cuboid measures 8 cm by 8 cm by 2 cm, and the cube sits on the 8 cm by 8 cm face.

Work out the total surface area of the solid.

8 cm8 cm2 cm4 cmDiagram NOT accurately drawn
4 marks
Show answer
256 cm²
8

A solid cylinder has a radius of 6 cm and a height of 5 cm.

  1. Work out the volume of the cylinder. Give your answer in terms of π.
  2. Work out the total surface area of the cylinder. Give your answer in terms of π.
4 marks
Show answer
a) 180π cm³ b) 132π cm²
9

A closed wooden box is a cuboid measuring 40 cm by 25 cm by 20 cm.

Amira varnishes all 6 faces of each box.

One tin of varnish covers 5000 cm2.

Amira has 3 tins of varnish.

Work out the greatest number of boxes Amira can varnish completely.

4 marks
Show answer
3
10

A closed cylindrical water tank has radius 40 cm and height 90 cm.

One tin of paint covers 3.5 m2.

Is one tin of paint enough to paint the whole outside of the tank, including the top and bottom, with one coat? You must show your working.

4 marks
Show answer
Yes - the area is 3.27 m2
11

A cube has a total surface area of 384 cm2.

Work out the volume of the cube.

4 marks
Show answer
512 cm³
12

A cuboid has a square base of side 5 cm and height h cm.

The total surface area of the cuboid is 190 cm2.

Work out the volume of the cuboid.

5 marks
Show answer
175 cm³
13

A cuboid has a base measuring 8 cm by 5 cm.

The volume of the cuboid is 320 cm3.

Work out the total surface area of the cuboid.

5 marks
Show answer
288 cm²
14

A cuboid measures 9 cm by 3 cm by 4 cm.

A cube has sides of length 5 cm.

  1. Show that the cuboid and the cube have the same total surface area.
  2. Which solid has the greater volume, and by how much?
5 marks
Show answer
a) both 150 cm2 b) cube by 17 cm3

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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