(Use $\pi = \frac{22}{7}$)
Sector Perimeter Calculation
The perimeter of a sector is calculated using the formula:
Perimeter = $2r + L$, where $r$ is the radius and $L$ is the arc length.
The arc length $L$ is given by:
$L = \frac{\theta}{360^\circ} \times 2\pi r$
Given:
- Radius ($r$) = $18\text{ cm}$
- Central angle ($\theta$) = $125^\circ$
- $\pi = \frac{22}{7}$
Arc Length Calculation
Substitute the given values into the arc length formula:
$L = \frac{125^\circ}{360^\circ} \times 2 \times \frac{22}{7} \times 18\text{ cm}$
Simplify the expression:
$L = \frac{125}{360} \times \frac{44}{7} \times 18\text{ cm}$
$L = \frac{25}{72} \times \frac{44}{7} \times 18\text{ cm}$
$L = \frac{25}{4} \times \frac{44}{7}\text{ cm}$
$L = 25 \times \frac{11}{7}\text{ cm}$
$L = \frac{275}{7}\text{ cm}$
Approximately, $L \approx 39.29\text{ cm}$.
Total Perimeter Calculation
Now, calculate the total perimeter using the formula Perimeter = $2r + L$:
Perimeter = $2 \times 18\text{ cm} + \frac{275}{7}\text{ cm}$
Perimeter = $36\text{ cm} + \frac{275}{7}\text{ cm}$
Perimeter = $\frac{36 \times 7}{7}\text{ cm} + \frac{275}{7}\text{ cm}$
Perimeter = $\frac{252}{7}\text{ cm} + \frac{275}{7}\text{ cm}$
Perimeter = $\frac{527}{7}\text{ cm}$
Approximate Perimeter
Calculate the final approximate value:
Perimeter $\approx 75.2857\text{ cm}$
Rounding to one decimal place, the approximate perimeter is $75.3\text{ cm}$.
Similar Questions
- The ratio of the length to the breath of a rectangular field is $6 : 5$. If the breath is 25 m less than the length, the perimeter of the field is:
- The ratio of the area of an equilateral triangle of side $x$ to the area of a square of side $x$ is:
- Find the perimeter of a semicircle with a radius of 7 cm. (Use $\pi = \frac{22}{7}$)
- What is the area of a rhombus, whose sides are 25 cm and one of the diagonals is 14 cm?
- Area of a square is equal to ten times the area of a rectangle of edge 5 cm $\times$ 8 cm. What is the perimeter of the square?
- If the length and the perimeter of a rectangle are in the ratio of 3 : 20, then its length and breadth will be in the ratio of:
- A wire in the form of a circle of radius 56 m is cut and again bent in the form of a square. What is the measure of the diagonal of the square?
- 30 ml paint is required to paint a circular plate of 20 cm radius. How much paint is required to paint a similar plate of radius 80 cm?
- The ratio of the radii of two circles is $1 : 4$. The ratio of their areas is:
- Which of the four options provided below will be the closest to the area of an equilateral triangle, each of whose sides is 10 m long?
Important Questions from 2-D Mensuration
- The sides of a rectangular field are 169 m and 154 m long. Its area is equal to the area of a circular field. What is the circumference (in m) of the circular field? Take $\pi = \frac{22}{7}$
- Find the area of a sector with a central angle of 150° in a circle with a radius of 12 cm.
- The area of a square is $2304$ cm$^2$. Its perimeter is equal to the perimeter of a regular hexagon. What is the area (in cm$^2$) of the hexagon?
Calculate the area of the triangle whose sides are 8 cm, 9 cm and 13 cm. (Rounded up to two decimal places)
- The length of a rectangular pitch is 30 m more than its breadth. Its area is $18,271$ m$^{2}$. Its breadth (in m) is:
