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
3111
If the length of a chord is 8 cm and its perpendicular distance from the center is 3 cm, find the radius of the circle.
Answer:
5 cm
A perpendicular from the center bisects the chord into two 4 cm segments. This forms a right triangle with legs of 3 cm (distance to center) and 4 cm (half chord). Using Pythagoras: r = √(3² + 4²) = √25 = 5 cm.
3112
A 2D shape has 4 sides. One pair of opposite sides is parallel, and the other pair is not. What is this shape called?
Answer:
Trapezium
A quadrilateral with exactly one pair of parallel sides is defined as a trapezium (or trapezoid in North American English).
3113
A certain polyhedron has 6 faces and 8 vertices. How many edges does it have?
Answer:
12
Using Euler's formula: F + V = E + 2. Substituting the given values: 6 + 8 = E + 2. So, 14 = E + 2, which means E = 12. A cube is a perfect example of such a polyhedron.
3114
Euler's formula relates the number of faces (F), vertices (V), and edges (E) of a polyhedron. Which of the following is correct?
Answer:
F + V = E + 2
Euler's formula for convex polyhedra states that the sum of the faces and vertices is exactly two more than the number of edges. This is mathematically expressed as F + V = E + 2.
3115
A triangular prism has a base area of 25 cm² and a length of 12 cm. What is its volume?
Answer:
300 cm³
The volume of any prism is calculated by multiplying the area of its base by its length (or height). Volume = base_area * length = 25 cm² * 12 cm = 300 cm³.
3116
What is the volume of a square-based pyramid with base side length 6 cm and vertical height 10 cm?
Answer:
120 cm³
The volume of a pyramid is V = (1/3) * base_area * height. The base is a square, so base_area = 6 * 6 = 36 cm². V = (1/3) * 36 * 10 = 12 * 10 = 120 cm³.
3117
A sphere and a cylinder have the same radius and the same volume. What is the height of the cylinder in terms of its radius 'r'?
Answer:
4r/3
Volume of sphere = Volume of cylinder. So, (4/3) * π * r³ = π * r² * h. Dividing both sides by π * r² gives (4/3) * r = h. The height of the cylinder is 4r/3.
3118
If the radius of a sphere is doubled, its volume becomes how many times the original volume?
Answer:
8 times
Volume of a sphere is proportional to the cube of its radius (r³). If the radius is doubled to 2r, the new volume becomes proportional to (2r)³ = 8r³. Therefore, the volume increases by a factor of 8.
3119
Find the total surface area of a solid hemisphere of radius 7 cm. (Use π ≈ 22/7)
Answer:
462 cm²
The total surface area of a solid hemisphere includes its curved surface (2πr²) and its flat circular base (πr²), summing to 3πr². Area = 3 * (22/7) * 7² = 3 * 22 * 7 = 66 * 7 = 462 cm².
3120
What is the volume of a hemisphere with a radius of 6 cm? (Leave answer in terms of π)
Answer:
144π cm³
The volume of a hemisphere is half the volume of a sphere: V = (2/3) * π * r³. Substituting r = 6 cm: V = (2/3) * π * 6³ = (2/3) * π * 216 = 2 * 72 * π = 144π cm³.