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Maths-

General

Easy

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 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 = $left parenthesis square root of 3 right parenthesis$ 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 cm³
As from the given condition ,
Volume of cube = volume of cuboid
a³= 27000
a = $cube root of 27000$
a = 30
Therefore the length of diagonal = $left parenthesis square root of 3 right parenthesis$ a
= $left parenthesis square root of 3 right parenthesis$ 30
= (1.734 )30
= 51.9
= 52
Therefore, the correct answer is d) 30cm , 52cm

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