Question

Find the values of $P,Q$ and $R$
(i) A circular pond is surrounded by a $2m$ wide circular path. If outer circumference of circular path is $44m$, then the area of the path is $\underset{–}{P}$.
(ii) A rectangular courtyard measuring $17m$ by $9\frac{1}{2}m$ is to be covered by square slabs, each of side $\frac{1}{2}m.\underset{–}{Q}$ slabs are required to cover the courtyard.
(iii) The minute hand of a circular clock is $15cm$ long. The tip of the minute hand move $\underset{–}{R}$ cm in $1$ hour?
(Take $\pi =3.14)$.

• A. $62.88m^2,348,100$
• B. $75.43m^2,646,94.2$
• C. $42.87m^2,200,44.5$
• D. $18.14m^2,544,79.4$

Answer 1

The correct option is B $75.43m^2,646,94.2$

Let $r$ and $R$ be the inner and outer radius of a circular pond respectively.
Outer circumference of the path $=44m$
i.e., $2\pi R=44$
$\Rightarrow 2\times \frac{22}{7}\times R=44\Rightarrow R=7m$
Inner radius, $r=(7-2)m=5m$
$\therefore$ Area of the path $=\pi R^2-\pi r^2$
$=\pi (R^2-r^2)=\frac{22}{7}(7^2-5^2)$
$=\frac{22}{7}(49-25)=\frac{22}{7}\times 24=75.43m^2$
(ii) Length of courtyard $=17m$
Breadth of courtyard $=9\frac{1}{2}m=\frac{19}{2}m$
Area of courtyard $=Length\times Breadth$
$=17\times \frac{19}{2}=\frac{323}{2}{m}^2$
Side of each square slab $=\frac{1}{2}m$
Area of one square slab $=(side{)}^2=\frac{1}{2}\times \frac{1}{2}=\frac{1}{4}{m}^2$
Required number of square slabs
$=\frac{\text{Area of courtyard}}{\text{Area of one slab}}=\frac{\frac{323}{2}}{\frac{1}{4}}=\frac{323}{2}\times =646$
(iii) Distance travelled by the tip of minute hand in $1hour=$ Circumference of the clock
$=2\pi r=2\times 3.14\times 15=94.2cm$.