Two cubes, each of volume 64 cm3, are joined end to end. Find the total surface area of the resulting cuboid.
Volumebof the cube = a3
Therefore,
a3 = 64
⇒ a3 = (4)3
⇒ a = 4
Each side of the cube = 4 cm
Then,
length of the cuboid ⇒ (2 × 4)
Breadth of the cuboid = 4 cm
Height of the cuboid = 4 cm
Total surface area of the cuboid = 2(lb+bh+lh)
=2[(8 × 4)+(4 × 4)+(8 × 4)]cm2
=(2 × 80) cm2
= 160 cm2
Concept: Concept of Surface Area, Volume, and Capacity
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2 cubes each of volume 64 cm 3 are joined end to end. Find the surface area of the resulting cuboid in cm 2
Solution
Let l be length of each cube
Volume of each cube = l3 =64 cm3
⇒ l3=64cm3
⇒ l = 4 cm
If, we join 2 cubes each having side equal to 4 cm, we get a cuboid
Length of cuboid= L=8 cm
Height of cuboid=H=4 cm
Breadth of cuboid=B=4 cm cm
We know that Surface Area of Cuboid =2(L.B+B.H+H.L)= 2((8x4)+(4x4)+(4x8))
=2(32+16+32)
= 2(80)
=160 cm2
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