3D Shapes — Quick Test

Two cubes, each with a side length of 4 cm, are stuck together to make a cuboid.

What is the volume of the cuboid?

• 128 cm³

• 64 cm³

• 256 cm³

• 32 cm³

• 16 cm³

Answer explanation

The volume of one cube is 4 × 4 × 4 = 64 cm³. The volume of the cuboid made from two cubes is 64 × 2 = 128 cm³.

Rob makes a cube with sides of length 2 cm out of card.

What is the area of the net that she needs to make the cube?

• 24 cm²

• 16 cm²

• 32 cm²

• 20 cm²

• 8 cm²

Answer explanation

The cube has side length 2 cm, so on the net, one face has area 2 × 2 = 4 cm².

There are six identical faces on a cube, so the total area is 4 × 6 = 24 cm².

A cuboid‑shaped container can hold 420 cm³ of water. It is 12 cm long and 7 cm wide.

What is the minimum height of the container?

• 5 cm

• 4 cm

• 8 cm

• 6 cm

• 7 cm

Answer explanation

Volume = length × width × height, so 420 = 12 × 7 × height = 84 × height. So height = 420 ÷ 84 = 5 cm (as 84 × 5 = 80 × 5 + 4 × 5 = 400 + 20 = 420).

Raj built the shape below using cubes with sides of length 2 cm.

What is the volume of the shape?

• 80 cm³

• 60 cm³

• 40 cm³

• 90 cm³

• 85 cm³

Answer explanation

The volume of one cube is 2 × 2 × 2 = 8 cm³. There are 10 cubes, so the shape’s volume is 8 × 10 = 80 cm³.

When this net is folded, how many faces will the 3D shape have?

• 7

• 5

• 3

• 8

• 6

Answer explanation

Count the number of shapes that form the net. There are 5 rectangles and 2 pentagons, so the 3D shape will have 7 faces.

What is the volume of a cube with sides of length 5 cm?

•  125 cm³

•  25 cm³

•  100 cm³

•  50 cm³

•  25 cm³

Answer explanation

The cube measures 5 cm × 5 cm × 5 cm. So its volume is 5 × 5 × 5 = 25 × 5 = 125 cm³­.

Which two of the nets below fold to make a triangle‑based pyramid?

• A and C

• C and D

• B and C

• A and D

• B and D

Answer explanation

It can’t be D because D has too many faces and it can’t be B because all four faces meet at one point. Only A and C fold to make a triangle­‑based pyramid.

Lucy built a model using identical cubes with sides of length 2 cm.

The volume of the model is 128 cm³.

How many cubes did she use?

• 16

• 12

• 8

• 10

• 4

Answer explanation

The volume of one cube is 2 × 2 × 2 = 8 cm³, so she used 128 ÷ 8 = 16 cubes (use short division).

The total area of all the faces of a cube is 150 cm².

What is the cube’s volume?

• 125 cm³

• 250 cm³

• 200 cm³

• 125 m³

• 25 cm³

Answer explanation

A cube has six identical square faces. If the total area of all these faces is 150 cm², then each face has an area of 150 ÷ 6 = 25 cm². 25 = 5 × 5, so the side length is 5 cm. Volume = (side length)³, so the volume of the cube is 5³ = 5 × 5 × 5 = 25 × 5 = 125 cm³.

A shape has 5 faces and 5 vertices. Four of the faces are identical to each other.

The other face is a regular quadrilateral.

What shape is it?

• Cylinder

• Square‑based pyramid

• Cuboid

• Triangle‑based pyramid

• Triangular prism

Answer explanation

A regular quadrilateral is a square. Square‑based pyramids have a square base with a triangular face joined to each edge of the square.