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
3071
A sector of a circle has an angle of 90 degrees and an area of 100π cm². What is the radius of the circle?
Answer:
20 cm
Sector area = (θ/360) * πr². Substituting the values: (90/360) * πr² = 100π. This simplifies to (1/4) * r² = 100. Multiplying by 4 gives r² = 400. Taking the square root, r = 20 cm.
3072
Two complementary angles are in the ratio 4:5. What is the measure of the larger angle?
Answer:
50 degrees
Complementary angles sum to 90 degrees. Let the angles be 4x and 5x. 4x + 5x = 90, so 9x = 90, meaning x = 10. The larger angle is 5x = 5 * 10 = 50 degrees.
3073
If a rectangular prism has dimensions 2x, 3x, and 4x, and its volume is 192 cm³, find the value of x.
Answer:
2 cm
Volume = length * width * height. Volume = (2x) * (3x) * (4x) = 24x³. We are given that 24x³ = 192. Dividing by 24 gives x³ = 8. Taking the cube root, x = 2 cm.
3074
The ratio of the volumes of two spheres is 8:27. What is the ratio of their surface areas?
Answer:
4:9
The volume of a sphere is proportional to r³. So, r1³ / r2³ = 8 / 27, meaning the ratio of their radii r1/r2 = 2/3. Surface area is proportional to r². Therefore, the ratio of surface areas is (2/3)² = 4/9.
3075
What is the centroid of a triangle?
Answer:
The point of intersection of its medians
The centroid is the geometric center of a triangle. It is formed by the intersection of the triangle's three medians (lines drawn from a vertex to the midpoint of the opposite side).
3076
A regular hexagon is inscribed in a circle of radius 6 cm. What is the perimeter of the hexagon?
Answer:
36 cm
A regular hexagon can be divided into 6 equilateral triangles emanating from the center. Therefore, the side length of the inscribed hexagon equals the radius of the circle. Side = 6 cm. Perimeter = 6 * side = 6 * 6 = 36 cm.
3077
What is the equation of a circle with a center at the origin (0,0) and a radius of 5?
Answer:
x² + y² = 25
The standard equation of a circle centered at the origin is x² + y² = r², where r is the radius. Substituting r = 5 gives x² + y² = 5² = 25.
3078
A cylindrical tank has a volume of 1540 m³ and a base radius of 7 m. Find its height. (Use π ≈ 22/7)
Answer:
10 m
Volume V = πr²h. 1540 = (22/7) * 7² * h. 1540 = 22 * 7 * h = 154h. Dividing both sides by 154 gives height h = 10 m.
3079
Find the area of a circle whose circumference is 10π cm.
Answer:
25π cm²
The circumference formula is C = 2πr. Here, 2πr = 10π, which simplifies to 2r = 10, or r = 5 cm. The area is A = πr² = π * 5² = 25π cm².
3080
The total surface area of a solid hemisphere is 108π cm². What is its radius?
Answer:
6 cm
The total surface area of a solid hemisphere is 3πr². Setting this equal to 108π: 3πr² = 108π. Dividing by 3π gives r² = 36. Therefore, the radius r = 6 cm.