Ex 12.1 Q1 - 2 cubes each of volume 64 cm³ are joined end to end. Find the surface area of the resulting cuboid.
Solution:-Given,
Volume of cube = 64 cm³
∴ (Edge)³ = (4 cm)³
∴ Edge = 4 cm
➙ When two cubes are joined end to end, the dimensions of the resulting cuboid will be,
length = l = 8 cm
breadth = b = 4 cm
height = h = 4 cm
Key Point: When two cubes are joined end to end, their lengths add up while the height and breadth remain unchanged.
Then, Surface area of resulting cuboid
= 2 [lb + bh + hl]
= 2 [8 × 4 + 4 × 4 + 4 × 8]
= 2 [32 + 16 + 32]
= 2 [80]
= 160 cm³
Hence,
The Surface area of the resulting cuboid will be 160 cm³.
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Try This..
✒ A cuboid is formed by joining 3 cubes each of volume 27 cm³. What is the surface area?
✒ Two cubes of side 6 cm are placed one above the other. Find the total surface area.
✒ What is the surface area when 3 cubes of side 5 cm are joined end to end?
❌ Common Mistakes
Forgetting to recalculate dimensions:▸ Just because you’re combining cubes doesn’t mean you use volume formula again. Update dimensions accordingly!Using cube formula for a cuboid:▸ After joining, it's a cuboid, not a cube anymore.Missing faces that become internal:▸ If asked total surface area, remember internal faces don’t count. (In this case, the internal face is hidden, but since we're calculating total surface area of resulting cuboid, we use the cuboid formula.)
📝 Related Questions:-
Queries Solved:-
Class 10 Ex 12.1
Ex 12.1 Q1 Class 10
Class 10 Ex 12.1 Q1
Class 10 Chap 12 Ex 12.1 Q1
Class 10 Surface Areas And Volumes
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