Question

the length,breadth and height of a rectangular solid are in the ratio 5 : 4 : 2 .If its total surface area is 1216 cm^3,find the volume of the solid.

Answer 1

Let length breadth and height be 5x, 4x and 2x respectively.

Now, T.S.A of solid=2 (lb + bh +lh)
2 (5x × 4x+4x×2x +5x ×2x )=1216
2 (20x^2+8x^2+10x ^2)=1216
2×38x^2=1216
38x^2=1216/2
x^2=608/38
x^2=16
x=4
so,length =5×=5×4=20cm
breadth=4×=4×4=16cm
height=2×=2×4=8cm

Answer 2

Let the length be 5x breadth be 4x and height be 2x
2(5x*4x + 5x*2x + 4x*2x ) = 1216
2(20x^2+10x^2+ 8x^2) = 1216
2* 38^2 = 1216
76x^2 = 1216
X^2 = 1216/76
X^2 = 16
X = 4
5x = 20
4x = 16
2x= 8
Volume = 20 * 16 * 8
= 2560 cm ^3

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