Question

4 identical cubes are joined end to end from a cuboid if the total surface area of the resulting cuboid is 648 cm find the length of each of each cube find the ratio between the surface area of the resulting cuboid and the surface area of the cube

Answer 1

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Answer 2

Answer:

The length of the side of the cube is 6 cm.

The ratio of area of cuboid and cube is 3 : 1.

Step-by-step explanation:

We are given that,

Total surface area of the cuboid = 648 cm²

Let the side of the cube = a cm.

So, we get,

The length of the cuboid = a + a + a + a = 4a cm.

The width of the cuboid = a cm.

Now, we have,

Total surface area of the cuboid = $2(lb+bh+hl)$

i.e. $648=2(4a\times a+a\times a+a\times 4a)$

i.e. $648=2(4a^2+a^2+4a^2)$

i.e. $648=2(9a^2)$

i.e. $648=18a^2$

i.e. $a^2=36$

i.e. a= 6 cm

Thus, the length of the side of the cube is 6 cm.

Further, we have,

Total surface area of the cuboid = 648 cm²

Total surface area of the cube = $6a^2$ = $6\times 6^2$ = 216 cm².

Thus, $\frac{A_{Cuboid}}{A_{Cube}}= \frac{648}{216}= \frac{3}{1}$

Hence, the ratio of area of cuboid and cube is 3 : 1.