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Question
A cuboidal block of solid iron has dimensions 50 cm, 45 cm and 34 cm. How many cuboids of size 5 cm by 3 cm by 2 cm can be obtained from this block? Assume cutting causes no wastage.
Solution
\[\text { Dimension of the cuboidal iron block = 50 cm }\times 45 cm \times 34 cm\]
\[\text { Volume of the iron block = length } \times\text { breadth \times\text { height }= (50 \times 45 \times 34) {cm}^3 = 76500 {cm}^3 \]
\[\text { It is given that the dimension of one small cuboids is 5cm } \times 3 cm \times 2 cm . \]
\[\text { Volume of one small cuboid = length } \times \text { breadth }\times \text { height } = (5 \times 3 \times 2) {cm}^3 = 30 {cm}^3 \]
\[ \therefore \text { The required number of small cuboids that can be obtained from the iron block } = \frac{\text { volume of the iron block}}{\text { volume of one small cuboid }} = \frac{76500 {cm}^3}{30 {cm}^3} = 2550\]
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