The dimensions of a cuboid are in the ratio 5 : 3 : 1 and its total su

1.	The dimensions of a cuboid are in the ratio 5 : 3 : 1 and its total surface area is 414 m2. Find the dimensions.
Answer» Given, Ratio of dimensions of cuboid = 5:3:1 Total surface area of cuboid = 414 m² Let dimensions are = 5x x 3x x x So, = 2(lb x bh x hl) = 414 = 2(15x² + 3x² + 5x²) = 414 = 2 x 23x² = 414 = x² = \(\frac{414}{46}\) = 9 = x = \(\sqrt9\) = 3 So, Dimensions are = 5x = 5 x 3 = 15 m = 3x = 3 x 3 = 9 m = x = 3 m

The dimensions of a cuboid are in the ratio 5 : 3 : 1 and its total surface area is 414 m2. Find the dimensions.

Answer»

Given,

Ratio of dimensions of cuboid = 5:3:1

Total surface area of cuboid = 414 m²

Let dimensions are = 5x x 3x x x

So,

= 2(lb x bh x hl) = 414

= 2(15x² + 3x² + 5x²) = 414

= 2 x 23x² = 414

= x² = \(\frac{414}{46}\) = 9

= x = \(\sqrt9\) = 3

So,

Dimensions are = 5x = 5 x 3 = 15 m

= 3x = 3 x 3 = 9 m

= x = 3 m