A cuboid with sides in the ratio 8:5:6 is cut perpendicular to its length to form three smaller cubo

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23 Mar 2022 Area and Volume

A cuboid with sides in the ratio 8:5:6 is cut perpendicular to its length to form three smaller cuboids of equal size. If sum of the surface areas of all three cuboids is 1080 cm² more than the surface area of original cuboid, then the volume of original cuboid (in cm³) is

OPtion

1) 4320
2) 5280
3) 6480
4) 6720
5) 6240
6) 7200
7) 6960
8) 5760
9) 7440
10) None of these

Solution

Let length, breadth & height of original cuboid be L, B, H respectively.
Then, its Curved Surface Area = 2(LB + BH + LH) -----(i)
Dimension of each new cuboid are L/3, B, H (Breadth and height being same)
Curved Surface Area of 3 new cuboids = 3*2[(L/3)B + BH + (L/3)H] = 2LB + 6BH + 2LH ---(ii)
Difference of Curved Surface Area (ii) - (i) = 4BH = 1080
BH = 270
Let Length, Breadth & Height of original cuboid be 8x, 5x, 6x respectively, then 5x*6x = 270
30x² = 270 or x = 3
So, sides of original cuboid are L=24 cm, B=15 cm, H=18 cm
.'. Volume of original cuboid = L*B*H = 24*15*18 = 6480 cm³.
Correct option 3)

Correct Option: 3 Best Solution (2)

G.S.Kantharao   2 years AGO

L,b,h=8x,5x,6x
Surface area=2(lb+bh+lh)
2(8x*5x+5x*6x+8x*6x)
=236x^2
Now smaller cuboid dimensions=8x/3,5x,6x
Surface area=2(40x^2/3+30x^2+16x^2)
Sum of 3 = 6(40+90+48)x^2/3=356x^2
Given=356x^2-236x^2=120x^2=1080=>x=3
L=24,b=15,h=18
Volume=24*15*18
=6480cm^3
My option is 3👈

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Mayank Kandoi   2 years AGO

For original cuboid,
Let, Length : Breadth : Height = 8x : 5x : 6x
Surface area = 2x² (40 + 30 + 48) = 236 x²

For new cuboids,
Dimensions = 8x/3 , 5x, 6x
Total surface area = 3 * 2x² ( 5×8/3 + 5×6 + 6×8/3) = 2x² (40 + 90 + 48) = 356 x²

Given, 236x² + 1080 = 356 x²
Hence, x = 3
Sides of original cuboid = 24, 15, 18
Volume of original cuboid = 24 × 15 × 18 = 6480

Option 3

Like? Yes (2) | No