Which one of the following is the area of a sector of a circle of radius 10 cm formed by an arc length of 15 cm?
$75 \text{ cm}^2$
Calculating Sector Area Using Arc Length
To find the area of a sector of a circle when the radius and arc length are known, we can use a direct formula.
Sector Area Formula
The area ($A$) of a sector is given by the formula:
$A = \frac{1}{2} \times \text{Arc Length} \times \text{Radius}$
Applying the Formula
Given:
- Radius ($r$) = 10 cm
- Arc Length ($L$) = 15 cm
Substitute these values into the formula:
$A = \frac{1}{2} \times L \times r$
$A = \frac{1}{2} \times 15 \text{ cm} \times 10 \text{ cm}$
Final Calculation
Perform the multiplication:
$A = \frac{1}{2} \times 150 \text{ cm}^2$
$A = 75 \text{ cm}^2$
Therefore, the area of the sector is $75 \text{ cm}^2$.
Important Questions from Area
What is the area of the triangle ABC with sides a = 10cm and c = 4cm angle B = 30°?
For the equations \(ax + (a^2 + 1)y = 4\) and \(4x + ay = a^2\), which of the following statements is TRUE?
What is the area of the parallelogram?
Consider the following statements :
1. If in a triangle ABC, A = 2B and b = c, then it must be an obtuse-angled triangle.
2. There exists no triangle ABC with A = 40°, B = 65° and a/c = sin 40° cosec 15°Which of the above statements is/are correct?
Consider the following statements in respect of the points (p, p - 3), (q + 3, q) and (6, 3):
1. The points lie on a straight line.
2. The points always lie in the first quadrant only for any value of p and q.
Which of the above statements is/are correct?
