Question

18. The cuboid shown below is made of 3 unit cubes like the one to its left: If the surface area of the cube is 18 sq. Cm, what is the surface area of the cuboid in sq. Cm?A)42b)48c)54d)81

Answer 1

The surface area of the cuboid is 42 sq.cm.

Explanation:

The cuboid is made of 3 unit cubes like the one to its left

Surface area of cube =
`6a^2`

Where a is the side of cube

We are given that surface area of cube is 18 sq.cm.

So,
`6a^2 = 18 \\a^2 = (18)/(6)\\a=\sqrt{(18)/(6)}\\a=√(3)`

Now these 3 cubes are joined together to form cuboid

So, Length of cuboid =
`√(3)+√(3)+√(3)=3√(3)`

Breadth of cuboid =
`√(3)`

Height of cuboid =
`√(3)`

Surface area of cuboid =
`2(lb+bh+hl)=2\left(3√(3)\cdot√(3)+√(3)\cdot√(3)+3√(3)\cdot√(3)\right)=42 cm^2`

Hence the surface area of the cuboid is 42 sq.cm.