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
181
What is the volume of a right circular cone with radius 6 cm and height 7 cm? (Use π ≈ 22/7)
Answer:
264 cm³
The volume of a cone is V = (1/3) * π * r² * h. Substituting the given values: V = (1/3) * (22/7) * 6² * 7 = (1/3) * 22 * 36 = 22 * 12 = 264 cm³.
182
The curved surface area of a cylinder is 264 cm² and its volume is 924 cm³. Find its height.
Answer:
6 cm
Volume / CSA = (πr²h) / (2πrh) = r/2. So, 924 / 264 = r/2. This gives 3.5 = r/2, so r = 7 cm. Using CSA to find height: 2 * (22/7) * 7 * h = 264. 44h = 264, meaning h = 6 cm.
183
If the radius of a cylinder is doubled and the height is halved, what happens to its volume?
Answer:
It is doubled
Original volume V = π * r² * h. New volume V' = π * (2r)² * (h/2) = π * 4r² * (h/2) = 2 * (π * r² * h) = 2V. The volume is doubled.
184
Two cylinders have equal volumes. Their heights are in the ratio 1:4. What is the ratio of their radii?
Answer:
2:1
Let V1 = V2, so π * r1² * h1 = π * r2² * h2. We are given h1/h2 = 1/4. Therefore, r1² / r2² = h2 / h1 = 4 / 1. Taking the square root, r1 / r2 = 2 / 1, giving a ratio of 2:1.
185
A cylindrical tank has a base circumference of 44 m and a height of 10 m. What is its lateral surface area?
Answer:
440 m²
The lateral (or curved) surface area of a cylinder is the product of its base circumference and height. Area = circumference * height = 44 m * 10 m = 440 m².
186
If the volume of a cylinder is 308 cm³ and its height is 8 cm, find its base radius. (Use π ≈ 22/7)
Answer:
3.5 cm
Volume = π * r² * h. 308 = (22/7) * r² * 8. This gives r² = (308 * 7) / (22 * 8) = 2156 / 176 = 12.25. Therefore, r = √12.25 = 3.5 cm.
187
What is the total surface area of a closed cylinder with radius 7 cm and height 13 cm? (Use π ≈ 22/7)
Answer:
880 cm²
Total Surface Area (TSA) of a closed cylinder = 2 * π * r * (r + h). Substituting the values: TSA = 2 * (22/7) * 7 * (7 + 13) = 44 * 20 = 880 cm².
188
Find the curved surface area of a solid cylinder of radius 5 cm and height 14 cm. (Use π ≈ 22/7)
Answer:
440 cm²
The curved surface area (CSA) of a cylinder is CSA = 2 * π * r * h. Substituting the values: CSA = 2 * (22/7) * 5 * 14 = 2 * 22 * 5 * 2 = 440 cm².
189
What is the volume of a cylinder with radius 7 cm and height 10 cm? (Use π ≈ 22/7)
Answer:
1540 cm³
The volume of a cylinder is V = π * r² * h. Substituting the given values: V = (22/7) * 7² * 10 = (22/7) * 49 * 10 = 22 * 7 * 10 = 1540 cm³.
190
If the volume of a cuboid is 360 cm³, and its base area is 45 cm², what is its height?
Answer:
8 cm
Volume of a cuboid = base area * height. We know Volume = 360 and Base Area = 45. To find height, divide Volume by Base Area: Height = 360 / 45 = 8 cm.