Exercises: Volume of a cuboid and nets

A cuboid measures $5$ cm by $4$ cm by $3$ cm. Find its volume.

How many faces, edges and vertices does a cuboid have?

A cube has edges of length $6$ cm.

1. a) Find its volume.

1. b) Find its total surface area.

A fish tank in a Galway aquarium shop is $80$ cm long, $40$ cm wide and $50$ cm high.

1. a) Find its volume in cm³.

1. b) Given that $1000$ cm³ $= 1$ litre, how many litres of water does it hold when full?

The net of a closed box is made of six rectangles. The box is $10$ cm long, $6$ cm wide and $4$ cm high.

1. a) List the dimensions of each pair of identical rectangles in the net.

1. b) Find the total area of the net.

A cuboid has volume $240$ cm³, length $10$ cm and width $6$ cm.

1. a) Find its height.

1. b) Find its total surface area.

A skip on a building site in Dublin is a cuboid $3$ m long, $1.5$ m wide and $1.2$ m deep (open top). It is filled with rubble to $\frac{2}{3}$ of its depth.

1. a) Find the volume of rubble in m³.

1. b) Each m³ of rubble has a mass of $1,600$ kg. Find the total mass in tonnes.

A cuboid has a square base of side $x$ cm and height $2x$ cm. Its volume is $432$ cm³.

1. a) Write an expression for the volume in terms of $x$.

1. b) Find $x$.

1. c) Find the total surface area.

A cube has edge $a$ cm. Each edge is doubled.

1. a) Show that the surface area is multiplied by $4$.

1. b) Show that the volume is multiplied by $8$.

1. c) A cube of edge $3$ cm has its edge tripled. By what factor does the volume change, and what is the new volume?