Two cubes each of volume 125 cm3 are joined end to end. Find the surface area of the resulting cuboid.
Answer: Each cube has side 5 cm, so the cuboid is 10 cm × 5 cm × 5 cm. Surface area = 2(50 + 25 + 50) = 250 cm2.
Step-by-step solution
Given: Two cubes, each of volume 125 cm3, joined end to end
To find: Surface area of the cuboid formed
To find: Surface area of the cuboid formed
Idea: Find the side of each cube, write the cuboid’s length, width and height, then use 2(lw + wh + hl).
- Side of each cube: a3 = 125 ⇒ a = 5 cm.½ mark
- Joined end to end: l = 5 + 5 = 10 cm, w = 5 cm, h = 5 cm.½ mark
- Surface area = 2(lw + wh + hl) = 2(10 × 5 + 5 × 5 + 5 × 10) = 2(50 + 25 + 50) = 2 × 125 = 250 cm2.1 mark
Surface area of the cuboid = 250 cm².
Check: Two separate cubes have 2 × 150 = 300 cm2. Joining hides two 5 × 5 faces: 300 − 50 = 250 cm2 ✓.
Answer to write in the exam
a3 = 125 ⇒ a = 5 cm
Cuboid: l = 10 cm, w = 5 cm, h = 5 cm
SA = 2(10 × 5 + 5 × 5 + 5 × 10) = 2 × 125
∴ Surface area = 250 cm2
Common mistakes that cost marks
- Adding the two cubes’ surface areas (300 cm2) and forgetting that the two joined faces are hidden.
- Taking the cuboid as 10 × 10 × 5.
How this can come in the exam
MCQ (1 mark)
Three cubes of side 4 cm are joined end to end. The surface area of the cuboid formed is
- 288 cm2
- 224 cm2
- 256 cm2
- 192 cm2
Show answer
(B) 224 cm2
Cuboid 12 × 4 × 4: 2(48 + 16 + 48) = 224 cm2.
Try one yourself
Two cubes each of volume 27 cm3 are joined end to end. Find the surface area of the cuboid.
Show answer
Side 3 cm; cuboid 6 × 3 × 3; SA = 2(18 + 9 + 18) = 90 cm2.
More questions like this
- A cube of side 4 cm is cut into cubes of side 1 cm. What is the ratio of the surface areas of the original cube and all the cut-out cubes? (Note that there is no change in volume but a big change in the surface area. This property has major consequences in the biological world.)
- 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?
- 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]