Area and Volume of Cube and Cuboid

Calculate the total surface area, in in², of the cuboid shown.

A cube has a surface area of 96cm².

Find the side length of the cube.

Answer explanation

$96\ \div\ 6\ =\ 16$

$\sqrt{16}\ =\ 4$

A cube has a surface area of 294 square centimeters. 
Find the side length, x, of the cube.

Answer explanation

 $296\ \div\ 6\ =\ 49$ 

 $\sqrt{49}\ =\ 7$ 

A company is designing a new box to hold cereal. They have two designs, cuboids A and B, with the same volume. The company wants to choose the smallest surface area.

Which cuboid should they choose?

• Cuboid A

• Cuboid B

• Either, they both have the same surface area.

A company is designing a new box to hold cereal. They have two designs, cuboids A and B, with the same volume. The company wants to choose the smallest surface area.

What is the difference, in cm², between the surface areas of the two boxes?

Answer explanation

Surface Area of Cuboid A is 184cm².

Surface Area of Cuboid A is 192cm².

The difference is 8cm².

The shapes are made from 1cm cubes.

What is the surface area, in cm², of the cube on the left-hand side?

Sue is covering this box with coloured paper.

She covers the two largest faces with blue paper.

Work out the area, in cm², of blue paper that she uses.

Answer explanation

30 x 20 = 600

600 x 2 = 1200 (2 largest faces)

Sue is covering this box with coloured paper.

She covers the two smallest faces with green paper.

Work out the area, in cm², of green paper that she uses.

Answer explanation

8 x 20 = 160

160 x 2 = 320 (2 smallest faces)

A cuboid is 9cm long.

It has square ends 2cm x 2cm.

Find, in cm², its total surface area.

The surface area of a cube is 150cm².

Work out, in cm², the area of one face.

Answer explanation

150cm² / 6 = 25cm²