Volume of a cuboid

A box has a length of 8 cm, a breadth of 5 cm and a height of 3 cm. Find the volume of the box. Here's the box. 8 centimetres long, 5 centimetres across, and 3 centimetres high. Volume is how much space is inside the box. Cut off one layer, one centimetre thick. One layer is the floor of the box, one centimetre high. The floor is covered in centimetre squares. 8 squares along the front, and 5 rows going back. That floor is the base area. So the volume is the floor, times the number of layers. Length times breadth times height. This box is 8, by 5, by 3. 8 times 5 is 40, so that's 40 squares, 3 layers deep. 40 times 3 is one hundred and twenty cubic centimetres.

Your turn. A solid is made from two rectangular boxes joined together, as shown. The lower box has a length of 10 cm, a breadth of 6 cm and a height of 4 cm. The upper box has a length of 5 cm, a breadth of 6 cm and a height of 3 cm. Find the volume of the solid. Try it first. Pause if you like. Same rule, and the same first line. Volume is length times breadth times height. Take the two boxes one at a time. The volume of the lower box is 10 times 6 times 4. That's two hundred and forty. And the volume of the upper box is 5 times 6 times 3. That's 90. So the total volume of the two boxes is two hundred and forty plus 90. That's three hundred and thirty cubic centimetres. A volume is a floor of squares, stacked. The floor is the length times the breadth. The height is how many floors there are. Two boxes joined are two volumes added. And the upper box is floors of squares too. Its floor is 5 by 6, and it is 3 floors high.