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Q.

Three smaller metal cubes are created by melting a larger cube of metal with a 12 cm edge. If the two smaller cubes' edges are 6 cm and 8 cm, respectively.

What is the edge of the third smaller cube?

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a

10 cm

b

12 cm

c

34 cm

d

67 cm

answer is A.

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Detailed Solution

Given that, a metal cube of edge 12 cm is melted and formed into three smaller cubes.
The edges of the two smaller cubes are 6 cm and 8 cm.
To find the edge of the third smaller cube.
The volume of the cube

= l 3

where l is the edge of the cube.
First, we will determine the volume of the bigger cube-

⇒ V = l 3 ⇒ V = 123 ⇒ V = 1728 cm 3

Now, we will find the volume of the smaller cube-

⇒ 63 = 216

⇒ 83 = 512

Now, we will find the volume of the third cube.
Volume of the large cube = Sum of the volume of smaller cubes
Let’s assume that the edge of the third cube is x then,

⇒ 1728 = 216 + 512 + x 3

⇒ x 3 = 1728 − (216 + 512)

⇒ x 3 = 1000

After taking cube roots on both the sides, we get,

∴ x = 10

Thus, the edge of the third smaller cube is 10 cm.
Hence, option 1 is the correct option.

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