Circles Quiz

Answer explanation

The correct formula to calculate the area of a circle with radius r is πr^2, as it involves squaring the radius and multiplying by π.

If the diameter of a circle is 10 cm, what is its area?

Answer explanation

The area of a circle is calculated using the formula A = πr^2. Since the diameter is 10 cm, the radius is half of that, which is 5 cm. Substituting the radius into the formula gives A = 25π cm^2.

Answer explanation

The length of an arc of a circle is calculated using the formula: length = (angle/360) * 2 * pi * radius. Substituting the values, we get (45/360) * 2 * pi * 7 = 7pi/4 cm. Therefore, the correct answer is 7pi/4 cm.

Answer explanation

The area of a sector is calculated using the formula A = (θ/360) * π * r^2. Substituting θ = 60° and r = 12 cm, we get A = (60/360) * π * 12^2 = 8π cm^2.

Answer explanation

Answer Explanation highlighting the correct choice: The length of an arc with a central angle of 90° in a circle with a radius of 10 cm is 1/4 of the circumference, which is 5π cm.

Answer explanation

The area of a sector of a circle is calculated using the formula (θ/360) * π * r^2. Substituting the values, we get (30/360) * π * 8^2 = 4π/3 cm^2, which is the correct choice.

A tangent line touches a circle at exactly how many points?

• 0

• 1

• 2

• It depends on the circle's radius.

Answer explanation

A tangent line touches a circle at exactly 1 point. This is a geometric property of tangency between a line and a circle.

If a secant line intersects a circle, how many points does it pass through on the circle?

• 1

• 2

• 3

• It varies based on the secant's angle.

Answer explanation

A secant line intersects a circle at two points, forming a chord. Therefore, it passes through 2 points on the circle.

Answer explanation

The correct formula for the length of an arc of a circle with radius r and central angle θ is l = rθ.

Answer explanation

The correct formula for calculating the area of a sector of a circle is A = \frac{1}{2}r^2\theta, which represents half the area of the corresponding circle based on the central angle.