Question

The surface area of a cylindrical box is $132{mm}^2$ and its height is $4mm.$ Find its radius.

• A. $2$ $mm$
• B. $3$ $mm$
• C. $4$ $mm$
• D. $5$ $mm$

Answer 1

Answer: (B)

$3$ $mm$

Given: Cylindrical box has surface area $A=132$ $m{m}^2$ and height $h=4mm$

We know surface area of cylinder is $A=2\pi r(r+h)$

Thus, $132=2\times \frac{22}{7}\times r(r+4)$

$\Rightarrow 132=\frac{44}{7}r(r+4)$

$\Rightarrow 132\times 7=44r(r+4)$

$\Rightarrow 924=44r^2+176r$

$\Rightarrow 44r^2+176r-924=0$

$\Rightarrow r^2+4r-21=0$

$\Rightarrow r^2+7r-3r-21=0$

$\Rightarrow r(r+7)-3(r+7)=0$

$\Rightarrow r+7=0,r-3=0$

$\Rightarrow r=-7,r=3$

Hence, the radius of the cylindrical box is $3$ mm.