MCQ
If a circle and a square have the same perimeter, then
- ATheir area are equal
- ✓Area of circle is larger
- CArea of square is larger
- DNone of these
$\therefore $ Let ‘$r$’ be the radius of circle and ‘$a$’ be the side of square
$\therefore $ $2\pi \,r = 4a \Rightarrow a = \frac{{\pi \,r}}{2}$
$\therefore $ Area of square ${C_1}(3,\; - 3)$ ${a^2} = \frac{{{\pi ^2}{r^2}}}{4}$
and area of circle = $\pi \,{r^2}$
$\therefore $ $\frac{{{\rm{Area\ of\ circle}}}}{{{\rm{Area\ of\ square}}}} = \frac{{\pi \,{r^2}}}{{{\pi ^2}{r^2}/4}} = \frac{4}{\pi } > 1$.
Thus, area of circle is larger than area of square.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
If $A_{k}=\sum_{i=0}^{9}\left(\begin{array}{l}9 \\ i\end{array}\right)\left[\begin{array}{c}12 \\ 12-k+i\end{array}\right]+\sum_{i=0}^{8}\left(\begin{array}{c}8 \\ i\end{array}\right)\left[\begin{array}{c}13 \\ 13-k+i\end{array}\right]$
and $A_{4}-A_{3}=190 \mathrm{p}$, then $p$ is equal to :