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Question

# Given length, breadth, and height of a cuboid are 15 cm, 37.5 cm, and 48 cm. Find the cube edge whose given volume is equal to the volume of this cuboid. Also, calculate the length of the diagonal to the nearest natural number.

- 32 cm , 52 cm
- 30 cm,50 cm
- 32 cm,50 cm
- 30 cm, 52 cm

Hint:

### Volume of a cuboid = length × breadth × height [cubic units]

or

Volume of a cuboid = l × b × h [cubic units]

Where,

- l = length
- b = breadth

h = height

Volume of cube:- a3 where a is side of cube.

Length of diagonal of cube = a

## The correct answer is: 30 cm, 52 cm

### We are given the dimensions of the cuboid

Length = l = 15cm

Breadth = b =37.5cm

Height = h = 48cm

Volume of a cuboid = l × b × h =

= 15 × 37.5 × 48

= 27000 cm^{3}

As from the given condition ,

Volume of cube = volume of cuboid

a^{3 }= 27000

a =

a = 30

Therefore the length of diagonal = a

= 30

= (1.734 )30

= 51.9

= 52

Therefore, the correct answer is d) 30cm , 52cm

^{3}

As from the given condition ,

Volume of cube = volume of cuboid

^{3 }= 27000

Therefore the length of diagonal = a

Therefore, the correct answer is d) 30cm , 52cm

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