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

Answer:

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

Step-by-step 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, $6a^2 = 18 \\a^2 = \frac{18}{6}\\a=\sqrt{\frac{18}{6}}\\a=\sqrt{3}$

Now these 3 cubes are joined together to form cuboid

So, Length of cuboid =$\sqrt{3}+\sqrt{3}+\sqrt{3}=3\sqrt{3}$

Breadth of cuboid = $\sqrt{3}$

Height of cuboid =$\sqrt{3}$

Surface area of cuboid =$2(lb+bh+hl)=2\left(3\sqrt{3}\cdot\sqrt{3}+\sqrt{3}\cdot\sqrt{3}+3\sqrt{3}\cdot\sqrt{3}\right)=42 cm^2$

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