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

 Exercise 14 F

Question 1 

Find the area of each circle. In question 1 take $\pi=3 \frac{1}{7}$ or $\frac{22}{7}$ and in question 2 , take $\pi$ 3.14 

(i) Area $=\pi r^{2}$

Sol:: $\frac{22}{7} \times 14^{2}$ $\frac{22}{7} \times 14 \times 14=616 \mathrm{~cm}^{2}$

(ii) Diameter = 56cm

Sol:  Radius = 28cm 

$\because$ Area $=\pi r^{2}=\frac{22}{7} \times 28 \times 28=2464 \mathrm{~cm}^{2}$

 

(iii) Diameter $=2 \frac{4}{5} \mathrm{~cm}=\frac{14}{5} \mathrm{~cm}$

Radius $=\frac{D}{2}=\frac{\frac{14}{5}}{2}=\frac{14}{5 \times 2}=\frac{14}{10} \mathrm{cm}$

Area $=\pi r^{2}=\frac{22}{7} \times \frac{14}{10} \times \frac{14}{10}$

$\frac{154}{25}$ or $6 \frac{4}{25} \mathrm{~m}^{2}$

(iv) $R=1 \frac{3}{4} \mathrm{~cm}=\frac{7}{4} \mathrm{~cm}$

Sol: Area = $\pi r^{2}=\frac{22}{7} \times \frac{7}{4} \times \frac{7}{4}=\frac{77}{8}=9, \frac{5}{8} \mathrm{cm}^{2}$

Question 2

(i) radius $=10 \mathrm{~cm}$ Take $=\pi=3 \cdot 14$

Sol:  Area $=\pi r^{2}$

$=3.14 \times 10 \times 10=314\operatorname{cm}^{2}$

(ii) $D=12 \mathrm{~mm}$

$R=6 \mathrm{~mm}$

Sol:  Area $=\pi r^{2}=3.14 \times 6 \times 6=113.04 \mathrm{mm}^{2}$

(iii) diameter $=30 \mathrm{~km}$

$R=15 \mathrm{~km}$

Sol: Area $=\pi r^{2}=3.14 \times 15 \times 15=706.5 \mathrm{~km}^{2}$

(iv) $R=0.5 \mathrm{~m}$

Sol: Area = $\pi r^{2}=3.14 \times 0.5 \times 0.5=0.785 \mathrm{~m}^{2}$

Question 3

Taking $\pi=\frac{22}{7}$, find the radii of the circles whose areas are

(i) $\frac{22}{7} \mathrm{~cm}^{2}$

Sol: Area $=\frac{22}{7} \mathrm{~cm}^{2}$

$\pi r^{2}=\frac{22}{7} \Rightarrow r^{2}=\frac{22}{7} \times \frac{7}{22} \quad \Rightarrow r^{2}=1$

 r=1cm answer 

(ii) Area $=154 \mathrm{~cm}^{2}$

Sol: $\pi r^{2}=154 \Rightarrow r^{2}=\frac{154}{22} \times 7 \Rightarrow r^{2}=7 \times 7$

r= 7cm answer 

(iii) Area $=314 \frac{2}{7} \mathrm{~mm}^{2}$  $[\because 314 \times 7=2193+2=2200]$

Sol: $\pi \pi^{2}=\frac{2200}{7}$ 

$r^{2}=\frac{2200}{7} \times \frac{7}{22} \Rightarrow r^{2}=100$

$\mathrm{r}=10 \mathrm{~mm}$ Answer 

Question 4

Taking $\pi=3.14$, find the diameters of the circles whose areas are

(i) $2826 \mathrm{~m}^{2}$

(ii) $7.065 \mathrm{~mm}^{2}$

(iii) $254.34 \mathrm{~cm}^{2}$

Sol: (i) Area $=2826 \mathrm{~m}^{2}$

$\pi r^{2}=2826 \Rightarrow r^{2}=\frac{2326}{3.14} \quad \Rightarrow r^{2}=900$

Taking square root r= 30 m Answer D= 60m answer 

Sol:(ii) Area = 7.065 $\mathrm{mm}^{2}$

=$\pi r^{2}=7.065$

=$\pi^{2}=\frac{7.065}{3.14}$

$=r^{2}=2.25$

$r=1.5 \mathrm{~mm}$

$D=3.0 \mathrm{~mm}$