Mathematics/General Ability MCQs
Topic Notes: Mathematics/General Ability
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
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
171
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.
172
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.
173
If the volume of a sphere is 288π cm³, what is its radius?
Answer:
6 cm
Volume = (4/3) * π * r³ = 288π. Dividing both sides by π gives (4/3) * r³ = 288. Multiply by 3/4 to isolate r³: r³ = 288 * (3/4) = 72 * 3 = 216. The cube root of 216 is 6, so r = 6 cm.
174
Find the surface area of a sphere of radius 7 cm. (Use π ≈ 22/7)
Answer:
616 cm²
The surface area of a sphere is calculated as Area = 4 * π * r². Substituting the values: Area = 4 * (22/7) * 7² = 4 * 22 * 7 = 88 * 7 = 616 cm².
175
What is the volume of a sphere with a radius of 3 cm? (Leave answer in terms of π)
Answer:
36π cm³
The volume of a sphere is V = (4/3) * π * r³. Substituting r = 3 cm: V = (4/3) * π * 3³ = (4/3) * π * 27 = 4 * 9 * π = 36π cm³.
176
A cylinder and a cone have the same base radius and the same height. What is the ratio of the volume of the cylinder to the volume of the cone?
Answer:
3:1
Volume of a cylinder = π * r² * h. Volume of a cone = (1/3) * π * r² * h. The ratio of their volumes is (π * r² * h) : ((1/3) * π * r² * h) = 1 : 1/3 = 3 : 1.
177
What is the total surface area of a right circular cone of radius 7 cm and slant height 13 cm? (Use π ≈ 22/7)
Answer:
440 cm²
Total Surface Area (TSA) of a cone = π * r * (r + l), where r is the radius and l is the slant height. TSA = (22/7) * 7 * (7 + 13) = 22 * 20 = 440 cm².
178
If the base area of a cone is 154 cm² and its height is 12 cm, what is its volume?
Answer:
616 cm³
The volume of a cone is V = (1/3) * Base Area * height. Substituting the given values: V = (1/3) * 154 * 12 = 154 * 4 = 616 cm³.
179
What is the curved surface area of a cone with radius 5 cm and slant height 10 cm? (Use π ≈ 3.14)
Answer:
157 cm²
The curved surface area (CSA) of a cone is calculated as CSA = π * r * l. Substituting the given values: CSA = 3.14 * 5 * 10 = 3.14 * 50 = 157 cm².
180
Find the slant height of a cone whose base radius is 3 cm and height is 4 cm.
Answer:
5 cm
The slant height (l) of a cone, its height (h), and its base radius (r) form a right-angled triangle. By Pythagoras: l = √(r² + h²) = √(3² + 4²) = √(9 + 16) = √25 = 5 cm.