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The volume of a packet containing 144 matchboxes is 2160 $c m 3$ . Then, the number of packets that can be placed in a carton of size 150 cm x 84 cm x 60 cm is ____.

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Detailed Solution

The volume of a packet containing 144 matchboxes is 2160

c m 3

. Then, the number of packets that can be placed in a carton of size 150 cm x 84 cm x 60 cm is 350.
Given that, the length of matchbox,

L = 4 c m

, the breadth of matchbox,

B = 2.5 c m

and the height of matchbox,

H = 1.5 c m

.
Volume of packet containing 144 matchboxes

= 2160 c m 3

Then, the volume of carton,

v = l × b × h

Substituting the value of

l = 150 c m

b = 84 c m

and

h = 60 c m

in the above formula.
We get,

v = 150 c m × 84 c m × 60 c m

v = 756000 c m 3

Total number of packets that can be placed in a carton

= V o l u m e of carton v o l u m e of  a packet

,
We get,

= 756000 c m 3 2160 c m 3

.
= 350.
Hence, 350 packets can be placed in a cartoon.

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