The dimensions of a cuboid are in the ratio 5:3:1and its total surface area is 414 m22 . Find the dimensions of the cuboid.
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The dimensions of a cuboid are in the ratio 5:3:1 and its total surface area is 414 m
2
. Find the dimensions of the cuboid.
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Dimensions of a cuboid are in the ratio=5:3:1
∴ length=l=5x
Breadth=b=3x and height=h=x
Total surface area of a cuboid=2(lb+bh+lh)
⇒414=2(5x×3x+3x×x+5x×x)
⇒414=2(15x
2
+3x
2
+5x
2
)
⇒414=2×23x
2
⇒207=23x
2
⇒x
2
=
23
207
=9
∴x=
9
=3
∴ Length=5x=5×3=15m
Breadth=3x=3×3=9m
and height=h=x=3m
The dimensions of the cuboid are 15m , 9m and 3 m if The dimensions of a cuboid are in the ratio 5:3:1and its total surface area is 414 m²
Given:
The dimensions of a cuboid are in the ratio 5:3:1
total surface area is 414 m²
To Find:
the dimensions of the cuboid.
Solution:
Surface area of the cuboid = 2(lb + bh + lh)
l = length , b = breadth , h = height
Step 1:
Assume that Sides in ratio 5:3: 1 are
l = 5x
b = 3x
h = x
in meters
Step 2:
Find Surface area and equate with 414
2( 5x * 3x + 3x*x + 5x * x) = 414
2(15x² + 3x² + 5x²) = 414
2(23x²) = 414
46x² = 414
Step 3:
Solve for x
46x² = 414
=> x² = 9
=> x = 3 ( as length can not be negative)
Step 4 :
Substitute x = 3 to find dimension
l = 5*3 = 15 m
b = 3*3 = 9 m
h = 3 m
The dimensions of the cuboid are 15m , 9m and 3 m if The dimensions of a cuboid are in the ratio 5:3:1and its total surface area is 414 m²