Find the total surface area of three cubes with each side 8 cm. If the three cubes are placed next to each other to form a cuboid, what will be the total surface area of the cuboid thus formed? What percentage has the total surface area increased or decreased with the new arrangement ?
Answers
Answer:
Total Surface Area (TSA) of cube = 6a^2
a = 8cm
TSA of cube = 6(8)^2
= 6(64)
= 384
TSA of 3 cube = 3 x 384
= 1152 → (1)
TSA of cuboid = 2 ( lb + bh + hl )
l = 24 cm
b = 8cm
h = 8 cm
TSA of cuboid = 2 [24(8) + 8(8) + 8(241) ]
= 2 [ 192 + 64 + 192 ]
=2 [448]
= 896 → (2)
Comparing (1) and (2) ,
(1) > (2)
the TSA of cuboid is decreased .
Since , to find the decreased percentage,
(2) - (1)
1152 - 896
= 256
Decreased percentage = 256/1152 x 100
= 22.22
hence, TSA of cube = 384
TSA of 3 cube = 1152
TSA of cuboid = 896
decreased percentage = 22.22%
Step-by-step explanation:
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