All Categories MCQs
Topic Notes: All Categories
General Description
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
3151
If the area of a circle is 154 cm², find its circumference. (Use π ≈ 22/7)
Answer:
44 cm
Area = π * r², so 154 = (22/7) * r². Thus, r² = 154 * (7/22) = 7 * 7 = 49, making r = 7 cm. The circumference C = 2 * π * r = 2 * (22/7) * 7 = 44 cm.
3152
A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the distance of the chord from the center of the circle.
Answer:
6 cm
A perpendicular drawn from the center to a chord bisects the chord. This creates a right-angled triangle where the hypotenuse is the radius (10), and one leg is half the chord length (8). Using Pythagoras: d² + 8² = 10², so d² + 64 = 100, meaning d² = 36. The distance d = 6 cm.
3153
If the circumference of a circle is 132 cm, what is its radius? (Use π ≈ 22/7)
Answer:
21 cm
The formula for circumference is C = 2 * π * r. We have 132 = 2 * (22/7) * r. This simplifies to 132 = (44/7) * r. To find r, multiply both sides by 7/44: r = 132 * (7/44) = 3 * 7 = 21 cm.
3154
Find the length of an arc of a circle with radius 21 cm corresponding to a central angle of 120 degrees. (Use π ≈ 22/7)
Answer:
44 cm
The length of an arc is given by the formula L = (θ / 360) * 2 * π * r. Substituting the values: L = (120 / 360) * 2 * (22/7) * 21 = (1/3) * 2 * 22 * 3 = 44 cm.
3155
What is the area of a sector of a circle with radius 6 cm and central angle 60 degrees? (Leave in terms of π)
Answer:
6π cm²
The formula for the area of a sector is (θ / 360) * π * r². Substituting the values: Area = (60 / 360) * π * 6² = (1/6) * π * 36 = 6π cm².
3156
Find the area of a circle with a diameter of 20 cm. (Use π ≈ 3.14)
Answer:
314 cm²
If the diameter is 20 cm, the radius (r) is 10 cm. The area of a circle is A = π * r². Substituting the values: A = 3.14 * (10)² = 3.14 * 100 = 314 cm².
3157
What is the circumference of a circle with a radius of 14 cm? (Use π ≈ 22/7)
Answer:
88 cm
The circumference of a circle is calculated using the formula C = 2 * π * r. Substituting the values: C = 2 * (22/7) * 14 = 2 * 22 * 2 = 88 cm.
3158
Which polygon has the same number of diagonals as its sides?
Answer:
Pentagon
We need n(n - 3) / 2 = n. Since a polygon must have n >= 3, we can divide both sides by n, giving (n - 3) / 2 = 1. Therefore, n - 3 = 2, which means n = 5. A pentagon has 5 sides and 5 diagonals.
3159
What is the sum of the exterior angles of a decagon?
Answer:
360 degrees
The sum of the exterior angles (one per vertex) of any simple convex polygon, regardless of the number of sides, is always 360 degrees.
3160
If an interior angle of a regular polygon is 150 degrees, how many sides does it have?
Answer:
12
If the interior angle is 150 degrees, the corresponding exterior angle is 180 - 150 = 30 degrees. The number of sides n = 360 / exterior angle. Thus, n = 360 / 30 = 12 sides.