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Example1

Title: Geometry

Grade Lesson s4-p1

Explanation: The best way to understand PSAT-4 is by looking at some examples. Take turns and read each example for easy understanding.

Examples

Topics → Definition Example1 Example2 Example3

An arc length in a circle is 6 cm, and the central angle corresponding to the arc is 40°. Find the radius of the circle.

Step: 1

The given arc length is 6 cm and the central angle is 40°.

To find the radius of the circle, we can use the formula relating the arc length, central angle, and radius:

arc length = radius \$\times\$ central angle

Explanation:

Here we have to find the radius(r) of the circle by using the arc length and central angle
arc length = radius \$\times\$ central angle.

Step: 2

Substituting these values into the formula, we have: \$6 cm = r \times 40°\$.

The angle to be in radians rather than°. Since 1 radian is equal to \$((180)°) / π\$, we can convert the angle to radians.

⇒ \$6cm = r \times ((40°)×(π/(180°)))\$

⇒ \$6 = r \times (2π)/9\$ radians

⇒ \$6/((2π)/9) = r\$ radians

⇒ \$r = (54cm)/ 2π\$ radians

⇒ \$r = (27cm) / π\$ radians

Thus, the radius of the circle is 8.6 cm.

Explanation:

Here, we substitute the given values in the formula. To find the circle’s radius, we substitute the π = 3.14. On solving, we get the radius of the circle is 8.6 cm.