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
3091
What is the maximum number of acute angles a convex polygon can have?
Answer:
3
If a convex polygon has an acute interior angle, its corresponding exterior angle must be obtuse (greater than 90 degrees). Since the sum of all exterior angles in any convex polygon is exactly 360 degrees, it can have at most three obtuse exterior angles (e.g., 3 * 100 = 300 < 360). Thus, it can have at most three acute interior angles.
3092
A cylindrical pipe has an inner diameter of 14 cm and water flows through it at 20 cm/sec. What is the volume of water flowing through per second? (Use π ≈ 22/7)
Answer:
3080 cm³
Inner radius r = 7 cm. The volume of water flowing per second is equivalent to the volume of a cylinder with r = 7 cm and height h = 20 cm. Volume = πr²h = (22/7) * 7² * 20 = 154 * 20 = 3080 cm³.
3093
An angle is 20 degrees more than its complement. What is the measure of the angle?
Answer:
55 degrees
Let the angle be x. Its complement is 90 - x. The problem states x = (90 - x) + 20. Solving for x gives 2x = 110, so x = 55 degrees.
3094
Find the area of a sector of a circle with a radius of 10 cm and an arc length of 15 cm.
Answer:
75 cm²
The area of a circular sector can be directly calculated from its arc length (L) and radius (r) using the formula Area = (1/2) * L * r. Substituting the values: Area = (1/2) * 15 * 10 = 75 cm².
3095
What is the formula for the volume of a frustum of a cone with radii r1 and r2, and height h?
Answer:
(1/3)πh(r1² + r2² + r1r2)
A frustum is a cone with its top cut off. Its volume is derived by taking the volume of the larger original cone and subtracting the volume of the smaller removed top cone, resulting in the formula V = (1/3)πh(r1² + r2² + r1r2).
3096
A circle is inscribed inside a square of side 14 cm. What is the area of the circle? (Use π ≈ 22/7)
Answer:
154 cm²
If a circle is inscribed in a square, its diameter equals the side of the square. Diameter = 14 cm, so radius r = 7 cm. Area = πr² = (22/7) * 7² = 22 * 7 = 154 cm².
3097
Which of the following describes a polygon with 10 sides?
Answer:
Decagon
In geometry, polygons are named based on their number of sides using Greek prefixes. A 10-sided polygon is called a decagon.
3098
If a right-angled triangle is revolved around its height, what 3D geometric shape is generated?
Answer:
Cone
Revolving a right-angled triangle a full 360 degrees around its vertical height sweeps out a solid shape known as a right circular cone, where the base of the triangle forms the circular base of the cone.
3099
What is the volume of a sphere whose surface area is 616 cm²? (Use π ≈ 22/7)
Answer:
1437.33 cm³
Surface Area = 4πr² = 616. 4 * (22/7) * r² = 616. r² = (616 * 7) / 88 = 7 * 7 = 49, so r = 7 cm. Volume = (4/3)πr³ = (4/3) * (22/7) * 7³ = (4/3) * 22 * 49 = 4312 / 3 ≈ 1437.33 cm³.
3100
A right circular cone has a base radius of 8 cm and a slant height of 10 cm. Find its vertical height.
Answer:
6 cm
In a cone, the radius, height, and slant height form a right triangle. Using Pythagoras: r² + h² = l². So, 8² + h² = 10², which gives 64 + h² = 100. h² = 36, meaning the vertical height h = 6 cm.