Question

Three equal cubes of sides 5cm each are placed to form a cuboid. Find the volume and the total surface area of the cuboid.

Answer 1

Given that:
Three cubes of equal side(l) = 5cm
Volume of 1 cube
= l³
= 5³
= 125cm³
Volume of 3 cubes
= 125 x 3
= 375cm³
Since, Volume of 3 cubes = Volume of cuboid
∴ Volume of cuboid = 375³
Now,
When the cubes are joined together, the breadth and height of the new cuboid
Formed remains the same whereas length changes.
Length of each cube = 5cm
∴ Length (l) of 3 cubes joined together
= 3 x 5cm
= 15cm
Breadth (b) of the new cuboid = 5cm
Height (h) of the new cuboid = 5cm
∴ T.S.A of the cuboid
= 2 x {(l x b) + (b x h) + (h x l)}
= 2{(15 x 5) + (5 x 5) + (5 x 15)]
= 2{75 + 25 + 75}
= 2 x 175
∴ T.S.A of cuboid = 350cm².