The volume of a cube is 64 cm³. What is its total surface area?

Step-by-step solution

Idea: First find the side from the volume (a³ = 64), then use TSA = 6a².

1. Let the side be a. Volume = a³ = 64, so a = ∛64 = 4 cm (since 4 × 4 × 4 = 64).1 mark
2. TSA = 6a² = 6 × 4² = 6 × 16 = 96 cm².1 mark

Check: A cube of side 4 cm: volume 64 cm³ ✓; each face 16 cm², six faces 96 cm² ✓.

Answer to write in the exam

Common mistakes that cost marks

• Taking the side as 64 ÷ 3 or √64 = 8 instead of the cube root ∛64 = 4.
• Using 4a² (only four faces) and getting 64 cm².

How this can come in the exam

Try one yourself

The volume of a cube is 343 m³. Find its total surface area.

More questions like this

• How many small cubes with side 20 cm can be packed tight in a cubical box with side 2 m?
• The dimensions of a godown are 40 m × 25 m × 10 m. If it is filled with cuboidal boxes, each of dimensions 2 m × 1.25 m × 1 m, then find the number of boxes.
• Two cubes each of volume 125 cm³ are joined end to end. Find the surface area of the resulting cuboid.
• A cube of side 4 cm is cut into cubes of side 1 cm. What is the ratio of the surface areas of the original cube and all the cut-out cubes? (Note that there is no change in volume but a big change in the surface area. This property has major consequences in the biological world.)
• The surface areas of the three faces of a cuboid that meet at one of the corners of the cuboid are 6 cm², 15 cm², and 10 cm² respectively. What is the volume of the cuboid?

All Surface area and volume questions · All maths questions