Question

A race track is in the form of a ring whose inner and outer circumference are $437m$ and $503m$ respectively. The area of the track is

• A. $66sq.m$
• B. $4935sq.m$
• C. $9870sq.m$
• D. None of these

Answer 1

Answer: (B)

$(4935sq.m)$

Let $r_1$ and $r_2$ be the radius of outer and inner circles then their corresponding circumference are $2\pi r_1=503$ and $2\pi r_2=437$

$\therefore r_1=\frac{503}{2\pi }$ and $r_2=\frac{437}{2\pi }$

Area of ring $=\pi (r_1^2-r_2^2)$
$=\pi (r_1+r_2)(r_1-r_2)$ [Since, $a^2-b^2=(a-b)(a+b)$]

$=\pi \left(\frac{503+437}{2\pi }\right)\left(\frac{503-437}{2\pi }\right)$

$=\frac{940}{2}\left(\frac{66}{2\pi }\right)$
$=235\times \frac{66}{22}\times 7$
$=235\times 21$
$=4935sq.m.$