The surface areas of the three faces of a cuboid that meet at one of the corners of the cuboid are 6 cm2, 15 cm2, and 10 cm2 respectively. What is the volume of the cuboid?
Answer: (lw)(wh)(hl) = (lwh)2 = 6 × 15 × 10 = 900, so volume = √900 = 30 cm3 (the cuboid is 2 cm × 3 cm × 5 cm).
Step-by-step solution
Given: Three faces at a corner: 6 cm2, 15 cm2, 10 cm2
To find: Volume of the cuboid
To find: Volume of the cuboid
Idea: The three faces at a corner are lw, wh and hl. Their product contains each edge twice, so it equals (volume)2.
- Let the edges be l, w, h. The three faces meeting at a corner have areas lw = 6, wh = 15, hl = 10.1 mark
- Multiply: (lw)(wh)(hl) = l2w2h2 = (lwh)2 = 6 × 15 × 10 = 900.1 mark
- Volume = lwh = √900 = 30 cm3 (volume is positive).1 mark
Volume = 30 cm³.
Check: Edges: h = 30 ÷ 6 = 5, l = 30 ÷ 15 = 2, w = 30 ÷ 10 = 3. Faces 2 × 3 = 6, 3 × 5 = 15, 5 × 2 = 10 ✓, and 2 × 3 × 5 = 30 ✓.
Answer to write in the exam
Let lw = 6, wh = 15, hl = 10
(lw)(wh)(hl) = (lwh)2
(lwh)2 = 6 × 15 × 10 = 900
∴ Volume = lwh = 30 cm3
Common mistakes that cost marks
- Adding the areas (31) or multiplying them (900) and calling that the volume. The product is the square of the volume.
- Taking the cube root of 900 instead of the square root.
How this can come in the exam
MCQ (1 mark)
The three faces of a cuboid meeting at a corner have areas 12 cm2, 20 cm2 and 15 cm2. Its volume is
- 47 cm3
- 3600 cm3
- 60 cm3
- 120 cm3
Show answer
(C) 60 cm3
√(12 × 20 × 15) = √3600 = 60 cm3 (edges 3, 4, 5).
Try one yourself
Three faces of a cuboid meeting at a corner have areas 8 cm2, 18 cm2 and 36 cm2. Find its volume.
Show answer
√(8 × 18 × 36) = √5184 = 72 cm3 (edges 2, 4, 9).
More questions like this
- A cube of side 5 cm is painted on all its faces. If it is sliced into 1 cm3 cubes, how many of these 1 cm3 cubes have
- Find a cuboid with edges whose lengths are integers (in cm), given that it has a total surface area of exactly 100 cm2.
- Suppose a swimming pool is being built in your school. Two choices are available for the dimensions of the pool: (A) 8 ft (depth) × 50 ft × 20 ft and (B) 6 ft (depth) × 100 ft × 15 ft. Which option would be suitable/appropriate for your school? Why? What parameters/aspects did you consider to make the choice? [1 cubic foot ≈ 28.3 litres]
- The following figures show different types of cylinders. What is different in each of these cylinders?
- What is the area of the curved surface of a cylinder?
Let the radius of the circular base of the cylinder be r; let its height be h. Suppose the cylinder is cut as shown in the figure below. We get a rectangle.