5. Seán loves reading books. He has 10 fi ction books, 15 comedy books and 8 true crime books. The dimensions of each type of book are provided in the table below.
(i) Sketch a drawing of each book, showing the length, width and height. (ii) Find the total volume of all his books combined.
Dimensions Length Width Height Total volume of one book
Fiction 23 cm 4 cm 18 cm
Comedy 24 cm 3·4 cm 120 mm True crime 20 cm 300 mm 11·5 cm
Total volume = ? 6. Large trucks often tow trailers that are shaped like rectangular solids.
A standard trailer is 13·6 m in length, 2·45 m in width and 2·60 m in height. Ignore the ‘thickness’ of the trailer walls.
(i) What is the greatest volume of cargo a standard trailer can hold? Give your answer to three decimal places.
(ii) How many complete trailers would it take to transport 300 m3 of goods?
(iii) Shane has a rectangular object with a length of 14·1 m, width of 2·3 m and height of 1·9 m. He thinks this volume is less than the volume of the truck trailer. Is he correct?
(iv) The truck driver states that this cargo will not fi t into his trailer. Do you agree? Justify your answer. 7.
If a carton of milk has a square base 10 cm wide and 10 cm long. What is the minimum height the carton must be to hold 2 litres of milk?
8. Three rectangular solids are shown in the diagram. (i) Find the volume, in cm3
, of each solid.
(ii) What do you notice about the three volumes?
(iii) Does the volume of a rectangular solid change if you place the solid on a diff erent base? Justify your answer.
9 cm 3 cm 6 cm 60 mm A 3 cm B
9. Calculate the volume of each of these solids. Hint: You can break each solid up into smaller rectangular solids.
(i) 9 m 11 m (iii) 5 m 6 m 4 m 4 m 1 cm 2 cm 3 cm 9 cm 5 cm 12 m 5 m 4 m 6 m 5 m (ii) 11 m 6 cm 30 mm C 90 mm 9 cm 1 000 cm3 = 1 litre