a cube and a cuboid have the same volume the demensions of the cuboid are in the ratio 1:2:4 if the difference between the cost of painting the cuboid and cube whole surface area at the rate 5 per sq m is rupees 80 find their volumes
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Answer:
Let each side of cube be
′
a
′
m.
Ratio of sides of cuboid is 1:2:4.
Let the sides be
′
x
′
m
Volume of cube= volume of cuboid
∴a
3
=x×2x×4x=8x
3
a
3
=8x
3
⇒a=2x
A/Q[6a
2
−2(lb+lh+bh)]×5=80
{6×(2x)
2
+2[2x
2
+8x
2
+4x
2
]}×5=80
⇒[−24x
2
+2(14x
2
)]×5=80
⇒(−24x
2
+28x
2
)×5=80
⇒4x
2
×5=80
⇒20x
2
=80
⇒x
2
=4
⇒x=2
∴a=2×2=4
∴ Volume of cube =(4)
3
=64m
3
sides of cuboid=x,2x,4x=2,4,8m
Volume of cuboid =2×4×8=64m
3
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