Maths-

General

Easy

Question

# A plate of 3 cm thick, 9 cm broad, and 27 m long is melted into a cube. find the difference in surface area of the two solids correct to the nearest whole number.

- 37
- 29
- 39
- 27

Hint:

### TSA of cuboid = 2[lb + bh + hl]

TSA of cube = 6x2

Volume of cube = x3

Volume of cuboid = l x b x h

Where , l is length, b is breadth , h is height

x is side of cube

## The correct answer is: 27

### We are given the dimensions of the plate

Thickness h = 3 cm

Breadth b= 9cm

Length l = 27cm

This plate is melted into cube , let x be the length of side of cube

So, as the plate is melted into cube the volume of both the solids will be same

Therefore, l x b x h = x^{3}

27 x 9 x 3 = x^{3}

729 = x^{3}

As we know, 729 is the cube of 9

Therefore, x = 9

Surface area of the plate = 2[lb + bh + hl]

= 2[(27)(9) + (9)(3) + (3)(27)]

= 2[243 + 27 + 81]

= 2(351)

= 702

Surface area of the cube = 6x^{2}

= 6(9)^{2}

= 6 (81)

= 486

Difference between both the areas= 702 – 486

= 216

Therefore the difference between the volumes is surface area .

^{3}

^{3}

As we know, 729 is the cube of 9

Therefore, x = 9

Surface area of the plate = 2[lb + bh + hl]

^{2}

^{2}

Difference between both the areas= 702 – 486

Therefore the difference between the volumes is surface area .

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