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Question
The weight of a metal block of size 5 cm by 4 cm by 3 cm is 1 kg. Find the weight of a block of the same metal of size 15 cm by 8 cm by 3 cm.
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Solution
\[\text { The weight of the metal block of dimension 5 cm }\times 4 cm \times 3 \text { cm is 1 kg } . \]
\[\text { Its volume = length } \times \text { breadth }\times \text { height } = (5 \times 4 \times 3) {cm}^3 = 60 {cm}^3 \]
\[\text { i . e . , the weight of 60 } {cm}^3\text { of the metal is 1 kg }\]
\[\text { Again, the dimension of the other block which is of same metal is 15 cm } \times 8 cm \times 3 cm . \]
\[\text { Its volume = length } \times \text { breadth } \times \text { height }= (15 \times 8 \times 3) {cm}^3 = 360 {cm}^3 \]
\[ \therefore \text { The weight of the required block } = 360 {cm}^3 \]
\[ = 6 \times 60 {cm}^3 ( \because \text { Weight of 60 }{cm}^3 \text { of the metal is 1Kg })\]
\[ = 6 \times 1 kg\]
\[ = 6 kg\]
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