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Volume and Surface Area of Solids — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSVolume and Surface Area of Solids5 Marks
Question
Find the volume of iron required to make an open box whose external dimensions are $36\ cm \times 25\ cm \times 16.5\ cm$, the box being $1.5\ cm $thick throughout. If $1cm^3$ of iron weighs $8.5$ grams, find the weight of the empty box in kilograms.
✓

Answer

Outer length of open box $= 36\ cm$
Breadth $= 25\ cm$
And height $= 16.5\ cm$
Thickness of iron $= 1.5cm.$
$\therefore$ Inner length $= 36 - 2 \times 1.5 = 36 - 3$
$= 33cm,$
Breadth $= 25 - 2 \times 1.5$
$= 25 - 3$
$= 22\ cm$ And height $= 16.5 - 1.5$
$= 15\ cm$
$\therefore$ Volume of iron used in it = Out volume - inner volume
$=36 \times 25 \times 16.5 cm^3-33 \times 22 \times 15 cm^3$
$= 14850 - 10890$
$=3960 cm^3$
Weight of $1cm^3 = 8.5$ gram
$\therefore$ Total weight
$= 3960 \times 8.5g$
$= 33660g$
$=33.660\ kg$
$= 33.66\ kg$

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