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A cubical box has each edge $ 10 \mathrm{~cm} $ and another cuboidal box is $ 12.5 \mathrm{~cm} $ long, $ 10 \mathrm{~cm} $ wide and $ 8 \mathrm{~cm} $ high.
(i) Which box has the greater lateral surface area and by how much?
(ii) Which box has the smaller total surface area and by how much?
Given:
A cubical box has each edge \( 10 \mathrm{~cm} \) and another cuboidal box is \( 12.5 \mathrm{~cm} \) long, \( 10 \mathrm{~cm} \) wide and \( 8 \mathrm{~cm} \) high.
To do:
We have to find:
(i) Which box has the greater lateral surface area and by how much and
(ii) Which box has the smaller total surface area and by how much.
Solution:
We have,
The edge of the cubical box $1$ $=10\ cm$
The length of the cuboidal box $2$ $l=12.5\ cm$
The breadth of the cuboidal box $2$ $b=10\ cm$
The height of the cuboidal box $2$ $h=8\ cm$
(i) The lateral surface area of cubical box $1=4(edge^2)$
$=4(10^2)$
$=4(100)$
$=400\ cm^2$
The lateral surface area of cuboidal box $=2(lh+bh)$
$=2(12.5\times8+10\times8)$
$=2(100+80)$
$=2(180)$
$=360\ cm^2$
Therefore,
The lateral surface area of the cubical box is more than the cuboidal box.
This implies,
$=(400-360)$
$=40\ cm^2$
Therefore, by $40\ cm^2$ cubical box has greater lateral surface area then cuboidal box.
(ii) We know that,
The total lateral surface area of the cubical box $=6(edge^2)$
This implies,
$=6(10^2)$
$=6(100)$
$=600\ cm^2$
The total lateral surface area of the cuboidal box $=2(lh+bh+lb)$
This implies,
$=2(12.5\times8+10\times8+12.5\times10)$
$=2(305)$
$=610\ cm^2$
Therefore,
The total lateral surface area of the cubical box is smaller than the cuboidal box
This implies,
$610-600=10\ cm^2$
Therefore, by $10\ cm^2$ cubical box has smaller lateral surface area then cuboidal box.