Question

find the ratio of volume of a cuboid to that of its original cuboid's volume, if its length is doubled, breadth is four times and height is reduced to half.
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Answer 1

Answer:

The ratio of the new cuboid to the original cuboid is 4: 1

Step-by-step explanation:

Let length, breadth and height of the original cuboid be l, b and h units respectively

New length, breadth and height of the cuboid after dimension are changed: length is doubled, breadth is four times and height is reduced to half

Length ( l' ) = 2 l units

Breadth ( b' ) = 4 b units

Height ( h' ) = $\frac{h}{2}$ units

Volume of the cuboid = length × breadth × height

Thus, ratio of new volume to the original volume of cuboid

            = New volume : Original Volume

            = l' × b' × h'  : l × b × h

            = 2 l × 4 b ×$\frac{h}{2}$     : l × b × h

            = 4 : 1

Hence, the required ratio is 4: 1