Measures and solids · Ages 14–15
Folding a box worksheet
Part of: Cones & spheres
In the print window, choose “Save as PDF” to download it. The answers print on the last page.
Folding a box worksheet
Measures and solids · Ages 14–15
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.A 21 cm × 14 cm sheet, as in the picture, has squares of side 3 cm cut from its corners and is folded into a box with no lid. The base is cm long and cm wide, and the box cm high.
Fill in each blank
Answer:
2.A 30 cm × 17 cm sheet, as in the picture, has a square of side 4 cm cut from each corner and is folded into a box with no lid. What is the box's volume, in cm³?
Answer:
3.A 23 cm × 16 cm sheet, as in the picture, has squares of side 4 cm cut from its corners and is folded into a box with no lid. The base is cm long and cm wide, and the box cm high.
Fill in each blank
Answer:
4.A 24 cm × 19 cm sheet has squares of side x cm cut from its corners and is folded into a box with no lid. In a table: x = 1 gives cm³, x = 2 gives cm³, x = 3 gives cm³.
Fill in each blank
Answer:
5.A square sheet of side 20 cm, as in the picture, has squares of side 5 cm cut from its corners and is folded into a box with no lid. How much does the box hold, in cm³?
Answer:
6.A square sheet of side 17 cm, as in the picture, has squares of side 4 cm cut from its corners and is folded into a box with no lid. How much does the box hold, in cm³?
Answer:
7.A square sheet of side 36 cm, as in the picture, has squares of side x cm cut from its corners (x a whole number) and is folded into a box with no lid. What x makes the box hold the most?
Answer:
8.A 28 cm × 27 cm sheet has squares of side x cm cut from its corners (x a whole number) and is folded into a box with no lid. What x makes the box hold the most?
Answer:
9.A 32 cm × 11 cm sheet has squares of side x cm cut from its corners (x a whole number) and is folded into a box with no lid. What x makes the box hold the most?
Answer:
10.A square sheet of side 30 cm, as in the picture, has squares of side x cm cut from its corners (x a whole number) and is folded into a box with no lid. What x makes the box hold the most?
Answer:
Part B: Choose, or true or false (2 marks each)
11.A square sheet of side 29 cm has squares of side 2 cm cut from its corners and is folded into a box with no lid. How long is a side of the box's base?
- A. 25 cm
- B. 21 cm
- C. 27 cm
- D. 29 cm
Choose the right answer
Answer:
12.From a 23 cm × 16 cm sheet, the box made by cutting 3 cm squares from the corners holds more than the box made by cutting 4 cm squares.
True or false?
Answer:
Part C: Word problems (4 marks each)
13.A 23 cm × 20 cm sheet has 3 cm squares cut from its corners and is folded into a lidless box. Find what it holds: put the steps in order.
- A. Base length = 23 − 2 × 3 = 17
- B. Volume = 238 × 3 = 714
- C. Base area = 17 × 14 = 238
Write the letters in the right order
Working:
Answer:
14.A 28 cm × 18 cm sheet has squares of side 5 cm cut from its corners and is folded into a box with no lid. Its base is cm × cm, and it holds cm³.
Fill in each blank
Working:
Answer:
15.A 23 cm × 12 cm sheet is folded into a lidless box with 2 cm or 3 cm squares cut from its corners. By how many cm³ do the two boxes differ?
Working:
Answer:
16.A factory cuts 6 cm × 6 cm from each corner of a square of cardboard 26 cm on a side and folds it into a lidless box for cookies. How many mL does the box hold?
Working:
Answer:
17.A 21 cm × 12 cm sheet has 3 cm squares cut from its corners and is folded into a lidless box. Find what it holds: put the steps in order.
- A. Base area = 15 × 6 = 90
- B. Base length = 21 − 2 × 3 = 15
- C. Volume = 90 × 3 = 270
Write the letters in the right order
Working:
Answer:
18.A 28 cm × 21 cm sheet has squares of side 4 cm cut from its corners and is folded into a box with no lid. Its base is cm × cm, and it holds cm³.
Fill in each blank
Working:
Answer:
Show the answers and working
Folding a box worksheet: Answers and working
Part A: Working out and filling in
1. 15, 8, 3
Each side loses 3 at both ends: 21 − 2 × 3 = 15, 14 − 2 × 3 = 8; the sides folded up are 3 high.
2. 792 cm³
The base is (30 − 2 × 4) × (17 − 2 × 4) = 22 × 9, the height 4: 792 cm³.
3. 15, 8, 4
Each side loses 4 at both ends: 23 − 2 × 4 = 15, 16 − 2 × 4 = 8; the sides folded up are 4 high.
4. 374, 600, 702
V = x(24 − 2x)(19 − 2x): put in x = 1, 2, 3 in turn.
5. 500 cm³
Base 10 × 10, height 5: 5 × 102 = 500 cm³.
6. 324 cm³
Base 9 × 9, height 4: 4 × 92 = 324 cm³.
7. 6 cm
Tabulate V = x(36 − 2x)2: it rises and then falls, greatest at x = 6 (3456 cm³) — a sixth of the side.
8. 5 cm
Tabulate V = x(28 − 2x)(27 − 2x) for x = 1, 2, 3, ...: it rises and then falls, its top at x = 5.
9. 2 cm
Tabulate V = x(32 − 2x)(11 − 2x) for x = 1, 2, 3, ...: it rises and then falls, its top at x = 2.
10. 5 cm
Tabulate V = x(30 − 2x)2: it rises and then falls, greatest at x = 5 (2000 cm³) — a sixth of the side.
Part B: Choose, or true or false
11. A. 25 cm
29 − 2 × 2 = 25 cm.
12. True
Cutting 3: 510 cm³; cutting 4: 480 cm³. A deeper cut makes a taller box but a smaller base, so not always a bigger one.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. A → C → B
The base's length and width, then its area, times the height 3: 714 cm³.
14. 18, 8, 720
28 − 2 × 5 = 18, 18 − 2 × 5 = 8; 5 × 18 × 8 = 720.
15. 2 cm³
Cutting 2 cm: 2 × (23 − 4) × (12 − 4) = 304; 3 cm: 3 × (23 − 6) × (12 − 6) = 306; 2 cm³ apart.
16. 1176 mL
Base 14 × 14, height 6: 1176 cm³ = 1176 mL.
17. B → A → C
The base's length and width, then its area, times the height 3: 270 cm³.
18. 20, 13, 1040
28 − 2 × 4 = 20, 21 − 2 × 4 = 13; 4 × 20 × 13 = 1040.
Numsprite · numsprite.com/en/worksheets/cones-and-spheres/folding-a-box-for-the-greatest-volume
Practise it in the gameFolding a box · Unlimited questions, no download