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Surface Area And Volume of A Cuboid And Cube — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsSurface Area And Volume of A Cuboid And Cube3 Marks
Question
How many cubic centimeters of iron are there in an open box whose external dimensions are $36\ cm, 25\ cm$ and $16.5\ cm$, the iron being $1.5\ cm$ thick throughout? If $1$ cubic cm of iron weighs $15\ gms$. Find the weight of the empty box in kg.
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Answer

Given:
Outer dimensions of iron:
Length $(l)=36 \mathrm{~cm}$
Breadth $(b)=25 \mathrm{~cm}$
Height $(h)=16.5 \mathrm{~cm}$
Inner dimensions of iron:
Length $(l)=36-(2 \times 1.5)=33 \mathrm{~cm}$
Breadth (b) $=25-(2 \times 1.5)=22 \mathrm{~cm}$
Height $(h)=16.5-1.5=15 \mathrm{~cm}$
Volume of Iron $=$ Outer volume - Inner volume
$=(36 \times 25 \times 16.5)-(33 \times 22 \times 15)$
$=3960 \mathrm{~cm}^3$
Weight of Iron $=3960 \times 15=59400$ grams $=59.4 \mathrm{kgs}$

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