If length, breadth and height of a cuboid are increased by 20%, what is the percentage increase in the the total surface area of cuboid? [3 MARKS]

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Solution

Concept: 1 Mark
Formula: 1 Mark
Application: 1 Mark

Let $l, b, h$ be the original dimensions

New dimensions
$= (1.2 l), (1.2 b), (1.2 h)$

New total surface area
$= 2 (l b + b h + h l)$

$= 2 (1.44 l b + 1.44 b h + 1.44 h l)$

$= 1.44 \times 2 (l b + b h + l h)$

$\Rightarrow 44 %$ increase in the total surface area.

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If length, breadth and height of a cuboid are increased by 20%, what is the percentage increase in the the total surface area of cuboid? [3 MARKS]

Concept: 1 Mark Formula: 1 Mark Application: 1 Mark Let l,b,h be the original dimensions New dimensions =(1.2l),(1.2b),(1.2h) New total surface area =2(lb+bh+hl) =2(1.44lb+1.44bh+1.44hl) =1.44×2(lb+bh+lh) ⇒44% increase in the total surface area.