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The volume of a cube whose edge measures 12 m is ____ times the volume of a cuboid of dimensions 8 m $\times$ 6 m $\times$ 4 m .

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Detailed Solution

The volume of a cube whose edge measures 12 m is 9 times the volume of a cuboid of dimensions 8 m

\times

6 m

\times

4 m .
Given the length of edge of the cube is 12 m.
Volume of cube is given by,

(s i d e) 3

.
So, the volume of the cube

= 12 \times 12 \times 12 = 1, 728 c m^{3}

Also given that the dimensions of cuboid are 8 m

\times

6 m

\times

4 m. The formula for the volume of cuboid having length, breadth and height as

l, b

and

h

respectively is given by,
Volume of a cuboid

= l \times b \times h

So, the volume of the cuboid

= 8 \times 6 \times 4 = 192 c m^{3}

Now,

\frac{1728}{192} = 9 times

Therefore, the volume of a cube whose edge measures 12 m is 9 times the volume of a cuboid of dimensions 8 m

\times

6 m

\times

4 m.

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