Question

How many cubic centimetres of iron are there in an open box whose external dimensions are 36m, 25cm and 16.5cm, the iron being 1.5cm throughout? If 1 cm³ of iron weight 15g find the weight of empty box in kilograms.

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Answer 1

$\huge\sf{ϙᴜᴇsᴛɪᴏɴ:-}$

How many cubic centimetres of iron are there in an open box whose external dimensions are 36m, 25cm and 16.5cm, the iron being 1.5cm throughout? If 1 cm³ of iron weight 15g find the weight of empty box in kilograms.

$\huge\sf{sᴏʟᴜᴛɪᴏɴ:-}$

$\green{\sf{The~external~length=36cm}}$

$\green{\sf{The~external~breadth=25cm}}$

$\green{\sf{The~external~height=16.5cm}}$

$\green{\boxed{\boxed{\sf{The~external~volume=Length×Breadth×Height}}}}$

$\green{\sf\leadsto{The~external~volume=36cm×25cm×16.5cm}}$

$\green{\sf{The~external~volume=14,850cm³}}$

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$\purple{\sf{The~internal~length=36-[2×1.5]}}$

$\purple{\sf{\leadsto{The~internal~length=33cm}}}$

$\purple{\sf{The~internal~breadth=25-[2×1.5]}}$

$\purple{\sf{\leadsto{The~internal~breadth=22cm}}}$

$\purple{\sf{The~internal~height=16.5-1.5}}$

$\purple{\sf{\leadsto{The~internal~height=15cm}}}$

$\purple{\sf{The~internal~volume=Length×Breadth×Height}}$

$\purple{\sf{\leadsto{The~internal~volume=33cm×22cm×15cm}}}$

$\purple{\sf{\leadsto{The~internal~volume=10,890cm³}}}$

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$\tt{\red{Volume~of~the~iron~box=14,850-10,890}}$

$\tt{\red{Volume~of~the~iron~box=3969cm³}}$

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$\orange{\sf{Weight~of~1m³~of~iron = 15grams}}$

$\orange{\sf{Weight~of~3960cm³~of~iron = (15×3960)=59400g}}$

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$\sf{\orange{1kg = 1000 g}}$

$\sf{\orange{\therefore59400g=\frac{594\cancel{00}}{10\cancel{00}}kg}}$

$\implies{\orange{\boxed{\boxed{\sf{59.4kg}}}}}$

The weight of empty box in kg = 59.4 kg

Answer 2

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