Mahabir Singh Solutions for Chapter: Perimeter and Area, Exercise 3: Exercise

A rectangular field is $112 \mathrm{m}$ long and $100 \mathrm{m}$ wide. Two roads, each $3 \mathrm{m}$ wide are to be constructed at the centre of the field; one is parallel to the length of the field and the other is parallel to the breadth of the field.

(i) Area of the part of the field, not covered by the roads.

(ii) Cost of constructing the road at $₹17$ per ${\mathrm{m}}^2$.

Which of the following statements is true?

 Statement$‐1$: A saree  $5.5 \mathrm{m}$ and $1.25 \mathrm{m}$ wide has a zari border $2.5 \mathrm{cm}$ broad along its length on either side. Along the width, on one edge the border was $5 \mathrm{cm}$ wide and on the other side the zari was $25 \mathrm{cm}$ wide. The area of the zari is $5855 {\mathrm{cm}}^2$.

Statement$‐2$: The moon is about $384000 \mathrm{km}$ from earth and its path around the earth is nearly circular. The length of path described by moon in one complete revolution will be $2,411,520 \mathrm{km}$. $(\mathrm{\pi }=3.14)$

Find the values of $P, Q$ and $R$.

$\left(\mathrm{i}\right)$ A circular pond is surrounded by a $2 \mathrm{m}$ wide circular path. If the outer circumference of circular path is $44 \mathrm{m}$, then the area of the path is $P$.

$\left(\mathrm{ii}\right)$ A rectangular courtyard measuring $17 \mathrm{m}$ by $9\frac{1}{2} \mathrm{m}$ is to be covered by square slabs, each of side $\frac{1}{2} \mathrm{m}$. $Q$ slabs are required to cover the courtyard.

$\left(\mathrm{iii}\right)$ The minute hand of a circular clock is $15 \mathrm{cm}$ long. The tip of the minute hand move $R$ $\mathrm{cm}$ in $1$ hour. $\left(\mathrm{\pi }=3.14\right)$