Find the number of cuboidal boxes measuring 2 cm

Question:

Find the number of cuboidal boxes measuring 2 cm by 3 cm by 10 cm which can be stored in a carton whose dimensions are 40 cm, 36 cm and 24 cm.

Solution:

Dimension of one cuboidal box $=2 \mathrm{~cm} \times 3 \mathrm{~cm} \times 10 \mathrm{~cm}$

Volume $=(2 \times 3 \times 10) \mathrm{cm}^{3}=60 \mathrm{~cm}^{3}$

It is given that the dimension of a carton is $40 \mathrm{~cm} \times 36 \mathrm{~cm} \times 24 \mathrm{~cm}$, where the boxes can be sto red.

$\therefore$ Volume of the carton $=(40 \times 36 \times 24) \mathrm{cm}^{3}=34560 \mathrm{~cm}^{3}$

$\therefore$ The required number of cuboidal boxes that can be stored in the carton $=\frac{\text { volume of the carton }}{\text { volume of one cuboidal box }}=\frac{34560 \mathrm{~cm}^{3}}{60 \mathrm{~cm}^{3}}=576$

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