Question

Find the volume of the cuboid if its surface area is 208 sq cm and the ratio of length, breadth and height is 2:3:4.

The answer is 15 but I donot know how did the answer come 15.

Answer 1

The volume of the cuboid is 192 cubic cm

Step-by-step explanation:

We are given that the ratio of length, breadth and height is 2:3:4.

Let the ratio be x

Length = 2x

Breadth = 3x

Height = 4x

Surface area of cuboid =$2(lb+bh+hl)=2(2x \times 3x + 3x \times 4x + 4x \times 2x)=52x^2$

We are given that its surface area is 208 sq cm

So,$52x^2 = 208$

$x^2 = \frac{208}{52}$

$x=\sqrt{\frac{208}{52}}$

x=2

Length = 2x =2(2)=4 cm

Breadth = 3x =3(2)=6 cm

Height = 4x=4(2)=8 cm

Volume of cuboid =$4 \times 6 \times 8 = 192 cm^3$

Hence the volume of the cuboid is 192 cubic cm

#Learn more:

The length , breadth , height of a cuboid are 4:3:2 . If its surface area is 2548 centimetre sq find its volume

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