A cube and a rectangular box has equal volume. It is given that the length and height of the rectangular box is 16 cm and 8 cm respectively. Also, if the side of the cube is 8 cm, what is the breadth of the rectangular box?

8 cm

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6 cm

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4 cm

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5 cm

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Solution

The correct option is C 4 cm
Given:
For rectangular box,
length = $16 c m$
height = $8 c m$
For cube, side = $8 c m .$
It is given that,
Volume of rectangular box = Volume of cube
$\Rightarrow l e n g t h \times b r e a d t h \times h e i g h t = s i d e^{3}$
$\Rightarrow 16 \times 8 \times b r e a d t h = 8^{3} = 512$
$\Rightarrow b r e a d t h = \frac{512}{16 \times 8} = 4 c m .$

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A cube and a rectangular box has equal volume. It is given that the length and height of the rectangular box is 16 cm and 8 cm respectively. Also, if the side of the cube is 8 cm, what is the breadth of the rectangular box?

The correct option is C 4 cmGiven: For rectangular box, length = 16 cm height = 8 cm For cube, side = 8 cm. It is given that, Volume of rectangular box = Volume of cube ⇒length×breadth×height=side3 ⇒16×8×breadth=83=512 ⇒breadth=51216×8=4 cm.