Question

The length breadth and height of a cuboid are in the ratio of 6:4:3. If the volume of cuboid is 576 cm", find out the total surface area of cuboid.​

Answer 1

Total Surface area of cuboid : 6912 cm²

Explanation:

Given:

1. The length breadth and height of a cuboid are in the ratio of 6:4:3

2. the volume of cuboid is 576 cm²

To find:

The total surface area of cuboid.​

Formula:

1. Total Surface area of cuboid : 2(l×b)+(l×h)+(b×h)

2. Volume of cuboid : length×breadth×height

length: breadth : height= 6:4:3

length = 6x

breadth = 4x

height = 3x

Volume of cuboid : l×b×h

volume of cuboid = 576 cm²

576 = (6x)×(4x)×(3x)

576 = 72x

72x =576

x=576/72

x = 8

Substitute x value

length = 6x

breadth = 4x

height = 3x

length = 48 cm

breadth = 32 cm

height = 24 cm

Total Surface area of cuboid : 2((l×b)+(l×h)+(b×h))

TSA = 2((48×32)+(48×24)+(32×24))

TSA = 2(1536+1152+768)

TSA = 2(3456)

Total Surface area of cuboid : 6912 cm²