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

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)

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

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.

RESOURCES

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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