Question

Three cubes each of side 6 cm are joined together side by side to form a cuboid.
(a) Find the surface area of the resultant cuboid.
(b) Is this surface area equal to the sum of the surface areas of the three separate cubes?

Answer 1

Answer:

a) 504$cm^{2}$

b) No

Step-by-step explanation:

a)

Given that 3 cubes of side 6cm join end to end.

So,

Length = 18cm, Width = 6cm and Height = 6cm

Surface area of cuboid = 2 * (lb + bh + lh)

= 2 * ( 18 * 6 + 6 * 6 + 18 * 6) = 2 * ( 216 + 36) = 2 * 252 = 504$cm^{2}$

Thus, the surface area of the cuboid is 504$cm^{2}$.

b)

Surface area of a cube is 6$a^{2}$, where a is equal to length.

So,

Surface area of 1 cube = 6 * 6 *6 = 216$cm^{2}$

Surface area of 3 cubes =  216$cm^{2}$ * 3 = 648$cm^{2}$

504$cm^{2}$ is not equal to 648$cm^{2}$ so no.

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