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Question
How many soap cakes can be placed in a box of size 56 cm × 0.4 m × 0.25 m, if the size of a soap cake is 7 cm × 5 cm × 2.5 cm?
Solution
\[\text { Dimension of a soap cake = 7cm } \times 5 cm \times 2 . 5 cm\]
\[\text { Its volume = length } \times \text { breadth } \times\text { height }= (7 \times 5 \times 2 . 5) {cm}^3 = 87 . 5 {cm}^3 \]
\[\text { Also, the dimension of the box that contains the soap cakes is 56 cm } \times 0 . 4 m \times 0 . 25 m, i . e . , 56 cm \times 40cm \times 25 cm ( \because 1 m = 100 cm) . \]
\[\text { Volume of the box = length } \times\text { breadth } \times \text { height }= (56 \times 40 \times 25) {cm}^3 = 56000 {cm}^3 \]
\[ \therefore\text { The number of soap cakes that can be placed inside the box }= \frac{\text { volume of the box }}{\text { volume of a soap cake }} = \frac{56000 {cm}^3}{87 . 5 {cm}^3} = 640\]
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