SChand Composite Mathematics Class 7 Chapter 14 Perimeter and Area Exercise 14E

 Exercise 14 E

Question 15

The circumference of the front wheel of a car  is 10 dm and that of the hind wheel in 16dm. How may revolutions more will the first wheel make than the second is covering a distance of 96 km?

Sol: Circumference of front wheel =10dm 

Circumference of back wheel = 16 dm 

Distance to be cover= 96 km or 9,60,000 dm

More no . of revolution by front  wheel = Rev. by front  wheel - Rev by back wheel 

 

$\left(\frac{960,000}{10}\right)-\left(\frac{960,000}{16}\right)$

$=96000-60,000$

=36000 

Question 16

There is a circular pond and foot- path runs along its boundary. A man walks around it, exactly once, keeping close to the edge. If his step is 55cm long and he takes exactly 400 steps to go round the pond . what is the diameter of the pond ? 

Sol: Circumference of the pond = $55 \times 400$ $=22,000 \mathrm{~cm}$ or 220 m 

$\left[\begin{array}{c}C=2 \pi r \\ \text { or } \\ \pi d\end{array}\right]$

$\pi d=220$

$d=\frac{220 \times 7}{22} \quad \Rightarrow d=70 \mathrm{cm}$

Question 17

A piece of wire is bent in the shape of an equilateral triangle of each side 6.6cm. It is rebent to form a circular ring. what is the diameter of the ring? 

[Hint. Perimeter of triangle $=$ Circumference of circular ring, i.e., $\pi \times d=3 \times 6.6]$

(image to be added )

Sol: Circumference of circular ring= Perimeter of triangle 

$\pi d=3 \times 6.6$

$d=\frac{3 \times 6.6}{22} \times 7 \Rightarrow d=6.3$ cm

Question 18

A wire is wound to form a circle of radius 56 cm. If the same wire is converted into a square. Find the side of this square. 

Sol: Perimeter of square = Circumference of circle 

$4 \times$ side $=2 \times \frac{22}{7} \times 56$

Side of the square = $2 \times \frac{22}{7} \times \frac{56}{4}=88 \mathrm{~cm}$