Introduction
On this article, we can be discussing the reply key for “Identify That Circle Half 1” quiz. This quiz is designed to check your data of circles and their properties. If you have not taken the quiz but, you could find it on-line and provides it a strive earlier than checking the reply key.
Query 1
The primary query within the quiz asks you to search out the realm of a circle with radius 5cm. The system to search out the realm of a circle is A = πr^2, the place r is the radius. Plugging within the values, we get A = π(5)^2 = 25π cm^2.
Which means the realm of the circle is 25π sq. centimeters.
Query 2
The second query asks you to search out the circumference of a circle with diameter 8cm. The system to search out the circumference of a circle is C = πd, the place d is the diameter. Plugging within the values, we get C = π(8) = 8π cm.
Which means the circumference of the circle is 8π centimeters.
Query 3
The third query asks you to search out the radius of a circle with space 36π cm^2. The system to search out the radius of a circle is r = √(A/π), the place A is the realm. Plugging within the values, we get r = √(36π/π) = 6cm.
Which means the radius of the circle is 6 centimeters.
Query 4
The fourth query asks you to search out the diameter of a circle with circumference 16π cm. The system to search out the diameter of a circle is d = C/π, the place C is the circumference. Plugging within the values, we get d = 16π/π = 16cm.
Which means the diameter of the circle is 16 centimeters.
Query 5
The fifth query asks you to search out the realm of a sector of a circle with radius 10cm and central angle 45°. The system to search out the realm of a sector of a circle is A = (θ/360)πr^2, the place θ is the central angle and r is the radius. Plugging within the values, we get A = (45/360)π(10)^2 = 12.5π cm^2.
Which means the realm of the sector is 12.5π sq. centimeters.
Query 6
The sixth query asks you to search out the size of an arc of a circle with radius 6cm and central angle 60°. The system to search out the size of an arc of a circle is L = (θ/360)2πr, the place θ is the central angle and r is the radius. Plugging within the values, we get L = (60/360)2π(6) = 2π cm.
Which means the size of the arc is 2π centimeters.
Query 7
The seventh query asks you to search out the equation of a circle with heart (2, -3) and radius 4. The system to search out the equation of a circle is (x – h)^2 + (y – okay)^2 = r^2, the place (h, okay) is the middle and r is the radius. Plugging within the values, we get (x – 2)^2 + (y + 3)^2 = 16.
Which means the equation of the circle is (x – 2)^2 + (y + 3)^2 = 16.
Query 8
The eighth query asks you to search out the middle of a circle with equation (x – 3)^2 + (y + 2)^2 = 25. The system to search out the middle of a circle is (h, okay), the place h and okay are the x and y coordinates of the middle. Evaluating the equation with the system, we get (h – 3)^2 = 25 and (okay + 2)^2 = 25. Fixing for h and okay, we get (h, okay) = (3, -2) or (8, -2).
Which means the middle of the circle is both (3, -2) or (8, -2).
Query 9
The ninth query asks you to search out the radius of a circle with equation (x – 2)^2 + (y + 4)^2 = 36. The system to search out the radius of a circle is r = √(a^2 + b^2), the place a and b are the coefficients of x and y within the equation. Plugging within the values, we get r = √(1^2 + (-4)^2) = √17.
Which means the radius of the circle is √17.
Query 10
The tenth query asks you to search out the equation of a circle with heart (-1, 5) and passing via the purpose (3, 3). The system to search out the equation of a circle is (x – h)^2 + (y – okay)^2 = r^2, the place (h, okay) is the middle and r is the radius. Plugging within the values, we get (3 – (-1))^2 + (3 – 5)^2 = r^2. Fixing for r, we get r = 4. Plugging within the values of (h, okay) and r, we get (x + 1)^2 + (y – 5)^2 = 16.
Which means the equation of the circle is (x + 1)^2 + (y – 5)^2 = 16.
Conclusion
In conclusion, we now have mentioned the reply key for “Identify That Circle Half 1” quiz. We hope this text has helped you perceive circles and their properties higher. Hold working towards and keep tuned for extra quizzes and reply keys.
