1. Cuboid Faces Based on https://nrich.maths.org/12466 Who took it from
South East Asian Mathematics Competition

2. Cuboid Faces
The faces of a cuboid have areas as shown in the diagram. What is the volume of the cuboid?
4 cm2
25 cm2
9 cm2
(not to scale)

3. 25 cm2 9 cm2 4 cm2 Cuboid Faces 𝒄 cm 𝒃 cm 𝒂 cm = 30 cm3 𝑎𝑐=4 𝑏𝑐=9
𝑎𝑏=25
Cuboid Faces
4 cm2
25 cm2
9 cm2
𝒄 cm
𝑎𝑏 𝑎𝑐 = ; 𝑏 𝑐 = ; 𝑏= 25 4 𝑐
𝑏𝑐=9 ; 𝑐 ×𝑐=9
𝑐 2 = 36 25
𝑐= ; 𝑏= ; 𝑎= 10 3
𝒃 cm
𝒂 cm
Volume of cuboid =𝑎𝑏𝑐
= × 15 2 × 6 5
= 30 cm3

4. 25 cm2 9 cm2 4 cm2 Cuboid Faces 𝒄 cm 𝒃 cm 𝒂 cm 𝑎𝑐=4 𝑏𝑐=9 𝑎𝑏=25
Alternatively, noting that if 𝑉 cm3 is the volume and that
𝑎𝑐×𝑏𝑐×𝑎𝑏= 𝑎 2 𝑏 2 𝑐 2 = 𝑎𝑏𝑐 2 = 𝑉 2
4×9×25= 𝑉 2
2×2 × 3×3 × 5×5 = 𝑉 2
So 𝑉=2×3×5=30 as before.

6. RESOURCES

7. SIC_64
Cuboid Faces
The faces of a cuboid have areas as shown in the diagram. What is the volume of the cuboid?
(not to scale)
150 cm2
3 cm2
2 cm2 A

8. SIC_64
Cuboid Faces
The faces of a cuboid have areas as shown in the diagram. What is the volume of the cuboid?
(not to scale)
90 cm2
5 cm2
2 cm2 B

9. SIC_64
Cuboid Faces
The faces of a cuboid have areas as shown in the diagram. What is the volume of the cuboid?
(not to scale)
75 cm2
6 cm2
2 cm2 C

10. SIC_64
Cuboid Faces
The faces of a cuboid have areas as shown in the diagram. What is the volume of the cuboid?
(not to scale)
50 cm2
9 cm2
2 cm2 D

11. SIC_64
Cuboid Faces
The faces of a cuboid have areas as shown in the diagram. What is the volume of the cuboid?
(not to scale)
45 cm2
10 cm2
2 cm2 E

12. SIC_64
Cuboid Faces
The faces of a cuboid have areas as shown in the diagram. What is the volume of the cuboid?
(not to scale)
30 cm2
15 cm2
2 cm2 F

13. SIC_64
Cuboid Faces
The faces of a cuboid have areas as shown in the diagram. What is the volume of the cuboid?
(not to scale)
25 cm2
18 cm2
2 cm2 G

14. SIC_64
Cuboid Faces
The faces of a cuboid have areas as shown in the diagram. What is the volume of the cuboid?
(not to scale)
75 cm2
4 cm2
3 cm2 H

15. SIC_64
Cuboid Faces
The faces of a cuboid have areas as shown in the diagram. What is the volume of the cuboid?
(not to scale)
60 cm2
5 cm2
3 cm2 I

16. SIC_64
Cuboid Faces
The faces of a cuboid have areas as shown in the diagram. What is the volume of the cuboid?
(not to scale)
50 cm2
6 cm2
3 cm2 J

17. SIC_64
Cuboid Faces
The faces of a cuboid have areas as shown in the diagram. What is the volume of the cuboid?
(not to scale)
30 cm2
10 cm2
3 cm2 K

18. SIC_64
Cuboid Faces
The faces of a cuboid have areas as shown in the diagram. What is the volume of the cuboid?
(not to scale)
25 cm2
12 cm2
3 cm2 L

19. SIC_64
Cuboid Faces
The faces of a cuboid have areas as shown in the diagram. What is the volume of the cuboid?
(not to scale)
20 cm2
15 cm2
3 cm2 M

20. SIC_64
Cuboid Faces
The faces of a cuboid have areas as shown in the diagram. What is the volume of the cuboid?
(not to scale)
45 cm2
5 cm2
4 cm2 N

21. SIC_64
Cuboid Faces
The faces of a cuboid have areas as shown in the diagram. What is the volume of the cuboid?
(not to scale)
25 cm2
9 cm2
4 cm2 O

22. SIC_64
Cuboid Faces
The faces of a cuboid have areas as shown in the diagram. What is the volume of the cuboid?
(not to scale)
30 cm2
6 cm2
5 cm2 P

23. SIC_64
Cuboid Faces
The faces of a cuboid have areas as shown in the diagram. What is the volume of the cuboid?
(not to scale)
20 cm2
9 cm2
5 cm2 Q

24. SIC_64
Cuboid Faces
The faces of a cuboid have areas as shown in the diagram. What is the volume of the cuboid?
(not to scale)
18 cm2
10 cm2
5 cm2 R

25. SIC_64
Cuboid Faces
The faces of a cuboid have areas as shown in the diagram. What is the volume of the cuboid?
(not to scale)
15 cm2
12 cm2
5 cm2 S

26. SIC_64
Cuboid Faces
The faces of a cuboid have areas as shown in the diagram. What is the volume of the cuboid?
(not to scale)
15 cm2
10 cm2
6 cm2 T