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 = x3
27 x 9 x 3 = x3
729 = x3
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 = 6x2
= 6(9)2
= 6 (81)
= 486
Difference between both the areas= 702 – 486
= 216
Therefore the difference between the volumes is surface area .
As we know, 729 is the cube of 9
Therefore, x = 9
Surface area of the plate = 2[lb + bh + hl]
Difference between both the areas= 702 – 486
Therefore the difference between the volumes is surface area .
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