Foundation June 2024 Paper 1R Q15
15 The diagram shows a box and a crate with a lid.
Diagram NOT accurately drawn
The box is a cube with sides of length 5 cm.
Tony has many boxes.
The crate is a cuboid with inside lengths of 27 cm, 35 cm and 40 cm.
Tony puts as many boxes as possible into the crate so that the lid will shut.
Work out the volume of space in the crate that is not filled up with boxes.
(4)
| Scheme | Marks |
|---|---|
| eg 35 ÷ 5 (= 7) or 27 ÷ 5 (= 5…) or 40 ÷ 5 (= 8) or 5 × 5 × 5 (= 125) or 27 × 35 × 40 (= 37 800) or 25 × 35 × 40 (= 35 000) | M1 |
| eg “7” × “5” × “8” (= 280) and 5 × 5 × 5 (= 125) or 27 – 5 × “5” (= 2) or 27 × 35 × 40 (= 37 800) and 25 × 35 × 40 (= 35 000) or (“37 800” ÷ “125”) – (“7” × “5” × “8”) (= 22.4) | M1 |
| “37 800” – “280” × “125” oe eg “37 800” – “35 000” or “2” × 35 × 40 or “22.4” × “125” | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: 2800 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for finding the number of boxes that fit along a side of the crate or the volume of the box or the volume taken up by the boxes
M1: for finding the total number of boxes that will fit in the crate and the volume of the box
or the number of cm remaining without a box
or the volume of the crate and the total volume of the boxes that fit
or the volume of space left at the top in terms of number of boxes
M1: for a fully correct method to find the volume of space left
A1: cao