Same pattern as Jack's cubes — large and small in a box. New numbers, new story. Try each one on paper, then check the working below — or watch it drawn out, the same way the problem above is.
Question 1
A caterer packs a rectangular tray-box tightly with 12 identical large ice blocks and some identical small ice cubes, so that cubes of the same size are stacked directly on top of each other, filling the box exactly to the brim. The figure shows the first layer of cubes packed in the box. (a) How many small ice cubes does the caterer have? (b) The volume of the box is 1536 cm³. The total volume of the 12 large ice blocks is 1/2 of the volume of the box. What is the length of one edge of the small ice cube?
Work it out on paper, then check below. ▶ See the working
Question 2
A chocolate factory packs a rectangular crate tightly with 18 identical large chocolate cubes and some identical small chocolate cubes, so that cubes of the same size are stacked directly on top of each other, filling the crate exactly to the brim. The figure shows the first layer of cubes packed in the crate. (a) How many small chocolate cubes are there? (b) The volume of the crate is 5625 cm³. The total volume of the 18 large cubes is 2/5 of the volume of the crate. What is the length of one edge of the small cube?
Work it out on paper, then check below. ▶ See the working
Question 3
A candle maker packs a rectangular storage box tightly with 27 identical large cube-shaped candles and some identical small cube-shaped candles, so that candles of the same size are stacked directly on top of each other, filling the box exactly to the brim. The figure shows the first layer of candles packed in the box. (a) How many small candles does he have? (b) The volume of the box is 37800 cm³. The total volume of the 27 large candles is 5/7 of the volume of the box. What is the length of one edge of the small candle?
Work it out on paper, then check below. ▶ See the working