Question

Calculate the perimeter and area of a quadrant of a circle whose radii are
i) 98
ii) 70
iii) 42
iv) 28

Answer 1

Hint: Perimeter can be defined as the total length of the boundary of a geometrical figure. Area can be defined as the space occupied by a flat shape or the surface of an object. So, using this definition we can easily solve our problem.

Complete step-by-step answer:
If a circle is drawn from the origin, then the quadrant of a circle can be defined as a portion of the circle which lies between the positive x-axis and positive y-axis.

In general, the perimeter of the quadrant of circle $={\displaystyle \frac{\pi r}{2}}+2r$.
The area of quadrant of a circle $={\displaystyle \frac{1}{4}}\pi r^2$.
i) Perimeter of quadrant of a circle of radius 98 cm $={\displaystyle \frac{\pi (98)}{2}}+2\times 98=350cm$
Area of quadrant of circle of radius 98 cm$={\displaystyle \frac{1}{4}}\times \pi \times {(98)}^2=7546c{m}^2$
ii) Perimeter of quadrant of a circle of radius 70 cm $={\displaystyle \frac{\pi (70)}{2}}+2\times 70=250cm$
Area of quadrant of circle of radius 70 cm$={\displaystyle \frac{1}{4}}\times \pi \times {(70)}^2=3850c{m}^2$
iii) Perimeter of quadrant of a circle of radius 42 cm $={\displaystyle \frac{\pi (42)}{2}}+2\times 42=150cm$
Area of quadrant of circle of radius 42 cm $={\displaystyle \frac{1}{4}}\times \pi \times {(42)}^2=1386c{m}^2$
iv) Perimeter of quadrant of a circle of radius 28 cm $={\displaystyle \frac{\pi (28)}{2}}+2\times 28=100cm$
Area of quadrant of circle of radius 28 cm $={\displaystyle \frac{1}{4}}\times \pi \times {(28)}^2=616c{m}^2$

Note: The key step for solving this problem is the knowledge of area and perimeter of a geometrical figure. In this case, the given figure is a quadrant of a circle. So, on constructing the figure we obtain the area and parameter in generalized form. After putting values in the formula, we get the desired result.