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Question
A cuboid is 25cm long, 15cm board and 9cm high. Find the whole surface of a cube having its volume equal to that of the cuboid.
Solution
Given that:
Length of the cuboid = 25cm
Breadth of the cuboid = 15cm
Height of the cuboid = 9cm &
Volume of cube = volume of cuboid
We know that volume of Cuboid
= l x b x h
= 25 x 15 x 9
= 375cm3
∴ Volume of cube = 3375cm3
But we know that volume of cube = l3
i.e.,
l3 = 3375
l = `root(3)(3375)`
= 15cm
∴ Side (l) = 15cm
Now,
T.S.A of cube
= 6l2
= 6 x 15 x 15
= 1350cm2.
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