Question:
The edge of the cuboid are in the ratio 1:2:3 and its surface area is 88cm2. Then the volume of the cuboid is
(a) 24 cm3
(b) 64 cm3
(c) 48 cm3
(d) 120 cm3
Answer:
Total surface area of a cuboid ,S = 2[ lb+bh+lh]
Given length ,breadth and height are in the ratio 1:2:3
Let the dimensions be x,2x and 3x
Volume ,V = lbh= x*2x*3x
S = 88 cm2
2[lb+bh+lh]=88
2[(x*2x)+(2x*3x)+(3x*x)]=88
(2x^2)+(6x^2)+(3x^2)=88/2
x^2(2+6+3)=44
x^2(11)=44
x^2=44/11
x^2=4
x=2
Volume = 2*(2*2)*(3*2)
=2*4*6
=48cm^3
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