Q1. Find the area of a circle whose radius is
(i) 7 cm
(ii) 2.1 m
(iii) 7 km
\begin{array}{l} \text {Sol. (i) We know that the area A of a circle of radius r } =\pi r^{2} \\ \text {Given radius r } =7 \text { cm} \\ \therefore \text {Area of circle (A) } =\frac{22}{7} \times 7 \times 7 =154 \text { cm}^{2} \\ \\\text {(ii) We know that the area A of a circle of radius r } =\pi r^{2} \\ \text {Given radius r } =2.1 \text { m} \\ \therefore \text {Area of circle (A) } =\frac{22}{7} \times 2.1 \times 2.1 =13.86 \text { m}^{2} \\ \\\text {(iii) We know that the area A of a circle of radius r } =\pi r^{2} \\ \text {Given radius r } =7 \text { km} \\ \therefore \text {Area of circle (A) } =\frac{22}{7} \times 7 \times 7 =154 \text { km}^{2} \\ \\\end{array}Q2. Find the area of a circle whose diameter is
(i) 8.4 cm
(ii)5.6 m
(iii) 7 km
\begin{array}{l} \text {Sol. (i) Given that diameter of circle } = 8.4 \text { cm} \\ \Rightarrow \text {Radius r } = \frac {8.4}{2} = 4.2 \text { cm} \\\text {We know that the area A of a circle of radius r } =\pi r^{2} \\ \therefore \text {Area of circle (A) } =\frac{22}{7} \times 4.2 \times 4.2 =55.44 \text { cm}^{2} \\ \\\text {(ii) Given that diameter of circle } = 5.6 \text { m} \\ \Rightarrow \text {Radius r } = \frac {5.6}{2} = 2.8 \text { m} \\\text {We know that the area A of a circle of radius r } =\pi r^{2} \\ \therefore \text {Area of circle (A) } =\frac{22}{7} \times 2.8 \times 2.8 =24.64 \text { m}^{2} \\ \\\text {(iii) Given that diameter of circle } = 7 \text { km} \\ \Rightarrow \text {Radius r } = \frac {7}{2} \text { km} \\\text {We know that the area A of a circle of radius r } =\pi r^{2} \\ \therefore \text {Area of circle (A) } =\frac{22}{7} \times \frac {7}{2} \times \frac {7}{2} =38.5 \text { km}^{2}\end{array}Q3. The area of a circle is 154 sq cm. Find the radius of the circle.\begin{array}{l} \text {Sol. Given that Area of circle } = 154 \text { cm}^{2} \\ \text {We know that the area A of a circle of radius r } =\pi r^{2} \\\therefore 154 =\frac{22}{7} r^{2} \\ \Rightarrow r^{2} = \frac {154 \times 7}{22}r^{2} \\ \Rightarrow r^{2} = 49 \\ \Rightarrow r = \sqrt {49} = \sqrt {7 \times 7} = 7 \text { cm} \\ \\\text { Q4. Find the radius of a circle, if its area is }\\ \text {(i) } \quad 4 \pi \text { cm}^{2} \quad \text {(ii) } \quad 55.44 \text { m}^{2} \quad \text {(iii)} \quad 1.54 \text { km}^{2} \end{array}\begin{array}{l} \text {Sol. } \\ \text {Sol. (i) Given that Area of circle } = 4 \pi \text { cm}^{2} \\ \text {We know that the area A of a circle of radius r } =\pi r^{2} \\\therefore 4 \pi =\pi r^{2} \\ \Rightarrow r^{2} = 4 \\ \Rightarrow r = \sqrt {4} = \sqrt {2 \times 2} = 2 \text { cm} \\ \\\text {(ii) Given that Area of circle } = 55.44 \text { m}^{2} \\ \text {We know that the area A of a circle of radius r } =\pi r^{2} \\\therefore 55.44 =\frac {22}{7} r^{2} \\ \Rightarrow r^{2} = 17.64 \\ \Rightarrow r = \sqrt {17.64} = \sqrt {\frac {1746}{100}} \text { m} \\ \Rightarrow r = \frac {42}{10} \text { m} \\ \Rightarrow r = 4.2 \text { m}\text {(iii) Given that Area of circle } = 1.54 \text { km}^{2} \\ \text {We know that the area A of a circle of radius r } =\pi r^{2} \\\therefore 1.54 =\frac {22}{7} r^{2} \\ \Rightarrow r^{2} = \frac {1.54 \times 7}{22} \\ \Rightarrow r^{2} = 0.49 \\ \Rightarrow r = \sqrt {0.49 } = \sqrt {\frac {49}{100}} \text { km} \\ \Rightarrow r = \frac {7}{10} \text { km} \\ \Rightarrow r = 0.7 \text { km}\end{array}Q5. The circumference of a circle is 3.14 m, find its area.
\begin{array}{l} \text {Sol. Given circumference of circle } =3.14 \text { m} \\ \text {(ii) We know that the circumference (C) of a circle having radius r } =2 \pi r \\ \Rightarrow 3.14 =2 \times 3.14 \times r \quad \quad [\text {Using :} \pi = 3.14] \\ \Rightarrow r = \frac {1}{2} =0.5 \text { m} \\\text {We know that the area A of a circle of radius r } =\pi r^{2} \\ \Rightarrow \text {Area of circle having radius 0.5 m} = 3.14 \times 0.5 \times 0.5= 0.785 \text { m}^{2} \\ \end{array}Q6. If the area of a circle is } 50.24 sq m, find its circumference.\begin{array}{l} \text {Sol. Given Area of circle } = 50.24 \text { m}^{2} \\ \text {We know that the area A of a circle of radius r } =\pi r^{2} \\ \Rightarrow 50.24 = \pi r^{2} \\ \Rightarrow r^{2} = \frac {50.24 \times 7}{22} = 15.985 \\ \Rightarrow r = \sqrt {15.985} = 3.998 \text { m} \\\text { We know that the circumference (C) of a circle having radius r } =2 \pi r \\ \Rightarrow C =2 \times \frac {22}{7} \times 3.998 \text { m} \\ \Rightarrow C =2 \times 3.142 \times 3.998 \text { m} \\ \Rightarrow C = 25.12 \text { m} \\\end{array}
(i) 7 cm
(ii) 2.1 m
(iii) 7 km
\begin{array}{l} \text {Sol. (i) We know that the area A of a circle of radius r } =\pi r^{2} \\ \text {Given radius r } =7 \text { cm} \\ \therefore \text {Area of circle (A) } =\frac{22}{7} \times 7 \times 7 =154 \text { cm}^{2} \\ \\\text {(ii) We know that the area A of a circle of radius r } =\pi r^{2} \\ \text {Given radius r } =2.1 \text { m} \\ \therefore \text {Area of circle (A) } =\frac{22}{7} \times 2.1 \times 2.1 =13.86 \text { m}^{2} \\ \\\text {(iii) We know that the area A of a circle of radius r } =\pi r^{2} \\ \text {Given radius r } =7 \text { km} \\ \therefore \text {Area of circle (A) } =\frac{22}{7} \times 7 \times 7 =154 \text { km}^{2} \\ \\\end{array}Q2. Find the area of a circle whose diameter is
(i) 8.4 cm
(ii)5.6 m
(iii) 7 km
\begin{array}{l} \text {Sol. (i) Given that diameter of circle } = 8.4 \text { cm} \\ \Rightarrow \text {Radius r } = \frac {8.4}{2} = 4.2 \text { cm} \\\text {We know that the area A of a circle of radius r } =\pi r^{2} \\ \therefore \text {Area of circle (A) } =\frac{22}{7} \times 4.2 \times 4.2 =55.44 \text { cm}^{2} \\ \\\text {(ii) Given that diameter of circle } = 5.6 \text { m} \\ \Rightarrow \text {Radius r } = \frac {5.6}{2} = 2.8 \text { m} \\\text {We know that the area A of a circle of radius r } =\pi r^{2} \\ \therefore \text {Area of circle (A) } =\frac{22}{7} \times 2.8 \times 2.8 =24.64 \text { m}^{2} \\ \\\text {(iii) Given that diameter of circle } = 7 \text { km} \\ \Rightarrow \text {Radius r } = \frac {7}{2} \text { km} \\\text {We know that the area A of a circle of radius r } =\pi r^{2} \\ \therefore \text {Area of circle (A) } =\frac{22}{7} \times \frac {7}{2} \times \frac {7}{2} =38.5 \text { km}^{2}\end{array}Q3. The area of a circle is 154 sq cm. Find the radius of the circle.\begin{array}{l} \text {Sol. Given that Area of circle } = 154 \text { cm}^{2} \\ \text {We know that the area A of a circle of radius r } =\pi r^{2} \\\therefore 154 =\frac{22}{7} r^{2} \\ \Rightarrow r^{2} = \frac {154 \times 7}{22}r^{2} \\ \Rightarrow r^{2} = 49 \\ \Rightarrow r = \sqrt {49} = \sqrt {7 \times 7} = 7 \text { cm} \\ \\\text { Q4. Find the radius of a circle, if its area is }\\ \text {(i) } \quad 4 \pi \text { cm}^{2} \quad \text {(ii) } \quad 55.44 \text { m}^{2} \quad \text {(iii)} \quad 1.54 \text { km}^{2} \end{array}\begin{array}{l} \text {Sol. } \\ \text {Sol. (i) Given that Area of circle } = 4 \pi \text { cm}^{2} \\ \text {We know that the area A of a circle of radius r } =\pi r^{2} \\\therefore 4 \pi =\pi r^{2} \\ \Rightarrow r^{2} = 4 \\ \Rightarrow r = \sqrt {4} = \sqrt {2 \times 2} = 2 \text { cm} \\ \\\text {(ii) Given that Area of circle } = 55.44 \text { m}^{2} \\ \text {We know that the area A of a circle of radius r } =\pi r^{2} \\\therefore 55.44 =\frac {22}{7} r^{2} \\ \Rightarrow r^{2} = 17.64 \\ \Rightarrow r = \sqrt {17.64} = \sqrt {\frac {1746}{100}} \text { m} \\ \Rightarrow r = \frac {42}{10} \text { m} \\ \Rightarrow r = 4.2 \text { m}\text {(iii) Given that Area of circle } = 1.54 \text { km}^{2} \\ \text {We know that the area A of a circle of radius r } =\pi r^{2} \\\therefore 1.54 =\frac {22}{7} r^{2} \\ \Rightarrow r^{2} = \frac {1.54 \times 7}{22} \\ \Rightarrow r^{2} = 0.49 \\ \Rightarrow r = \sqrt {0.49 } = \sqrt {\frac {49}{100}} \text { km} \\ \Rightarrow r = \frac {7}{10} \text { km} \\ \Rightarrow r = 0.7 \text { km}\end{array}Q5. The circumference of a circle is 3.14 m, find its area.
\begin{array}{l} \text {Sol. Given circumference of circle } =3.14 \text { m} \\ \text {(ii) We know that the circumference (C) of a circle having radius r } =2 \pi r \\ \Rightarrow 3.14 =2 \times 3.14 \times r \quad \quad [\text {Using :} \pi = 3.14] \\ \Rightarrow r = \frac {1}{2} =0.5 \text { m} \\\text {We know that the area A of a circle of radius r } =\pi r^{2} \\ \Rightarrow \text {Area of circle having radius 0.5 m} = 3.14 \times 0.5 \times 0.5= 0.785 \text { m}^{2} \\ \end{array}Q6. If the area of a circle is } 50.24 sq m, find its circumference.\begin{array}{l} \text {Sol. Given Area of circle } = 50.24 \text { m}^{2} \\ \text {We know that the area A of a circle of radius r } =\pi r^{2} \\ \Rightarrow 50.24 = \pi r^{2} \\ \Rightarrow r^{2} = \frac {50.24 \times 7}{22} = 15.985 \\ \Rightarrow r = \sqrt {15.985} = 3.998 \text { m} \\\text { We know that the circumference (C) of a circle having radius r } =2 \pi r \\ \Rightarrow C =2 \times \frac {22}{7} \times 3.998 \text { m} \\ \Rightarrow C =2 \times 3.142 \times 3.998 \text { m} \\ \Rightarrow C = 25.12 \text { m} \\\end{array}