Maths-

General

Easy

Question

# Given edges of the cubes as 3 cm, 4 cm, and 5 cm respectively. Its now melted and made into one single cube. Calculate the edge of a new cube.

- 3
- 6
- 9
- 12

Hint:

### Volume of cube = a3

where a is side of cube

If all three cubes are melted and made into one cube then the volume of all 3 cubes will be equal to volume of single cube made.

## The correct answer is: 6

### Let the cubes be A, B and C and their sides are x, y and z respectively

x= 3cm

y=4cm

z= 5cm

And let the side if final cube is w

We will first add the volumes of the three cubes A, B and C

Vol(A) + Vol(B) + Vol(C) = x^{3} + y^{3} + z^{3}

= 3^{3} + 4^{3} + 5^{3}

= 27 + 64 + 125

= 216

The sum of volumes of cubes A , B and C is equal to the resultant cube we obtain by melting these three,

Volume of final cube = Vol(A) + Vol(B) + Vol(C)

(w)^{3 }= 216

We know that 216 is the cube of 6

Therefore, w = 6

Therefore, the correct option is b) 6 .

And let the side if final cube is w

We will first add the volumes of the three cubes A, B and C

Vol(A) + Vol(B) + Vol(C) = x

^{3}+ y

^{3}+ z

^{3}

^{3}+ 4

^{3}+ 5

^{3}

The sum of volumes of cubes A , B and C is equal to the resultant cube we obtain by melting these three,

Volume of final cube = Vol(A) + Vol(B) + Vol(C)

^{3 }= 216

We know that 216 is the cube of 6

Therefore, w = 6

Therefore, the correct option is b) 6 .

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