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
2821
A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length of the wire.
Answer:
12.56 m
Diameter of wire = 3 mm = 0.3 cm. Number of turns = length of cylinder / diameter of wire = 12 cm / 0.3 cm = 40 turns. Length of wire per turn = circumference of cylinder = πd = π(10) = 10π cm. Total length of wire = 40 × 10π = 400π cm ≈ 400 × 3.1416 = 1256 cm = 12.56 meters.
2822
A rectangular water tank is 8 m high, 6 m long, and 2.5 m wide. How many liters of water can it hold?
Answer:
120,000 liters
Volume = L × W × H = 6 × 2.5 × 8 = 120 m³. Since 1 m³ holds 1000 liters, the capacity is 120 × 1000 = 120,000 liters.
2823
A room is 12 m long, 8 m wide, and 4 m high. What is the area of its four walls?
Answer:
160 m²
Area of four walls = Lateral Surface Area = 2h(l + w) = 2 × 4 × (12 + 8) = 8 × 20 = 160 m².
2824
The diameter of a sphere is 12 cm. What is its surface area in terms of π?
Answer:
144π cm²
Radius r = diameter / 2 = 12 / 2 = 6 cm. Surface area = 4πr² = 4 × π × 6² = 4 × 36 × π = 144π cm².
2825
Find the length of the arc of a circle of radius 21 cm which subtends an angle of 60° at the center. (Use π = 22/7)
Answer:
22 cm
Arc length = (θ/360) × 2πr = (60/360) × 2 × (22/7) × 21 = (1/6) × 2 × 22 × 3 = 22 cm.
2826
If the side of a square is increased by 20%, what is the percentage increase in its area?
Answer:
44%
Let the original side be 10. Area = 100. If the side increases by 20%, the new side is 12. The new area is 12² = 144. The increase is 144 - 100 = 44, which is a 44% increase.
2827
The parallel sides of a trapezium are 14 cm and 10 cm, and the distance between them is 5 cm. What is its area?
Answer:
60 cm²
Area of a trapezium = (1/2) × (Sum of parallel sides) × (distance between them). Area = (1/2) × (14 + 10) × 5 = (1/2) × 24 × 5 = 12 × 5 = 60 cm².
2828
A solid metal sphere of radius 3 cm is melted and the metal is used to form a solid cylinder of radius 2 cm. Find the height of the cylinder.
Answer:
9 cm
Volume of sphere = (4/3)πr³ = (4/3)π(3³) = 36π cm³. Volume of cylinder = πr²h = π(2²)h = 4πh. Equating the volumes: 4πh = 36π, which gives h = 9 cm.
2829
If the lengths of the diagonals of a rhombus are 16 cm and 12 cm, what is its area?
Answer:
96 cm²
The area of a rhombus is given by (1/2) × d1 × d2, where d1 and d2 are the lengths of the diagonals. Area = (1/2) × 16 × 12 = 96 cm².
2830
The height of a conical tent is 14 m and its floor area is 346.5 m². How much canvas, 1.1 m wide, will be required to make it? (Use π = 22/7)
Answer:
525 m
Base area = πr² = 346.5 => (22/7)r² = 346.5 => r² = 110.25 => r = 10.5 m. Slant height l = √(r² + h²) = √(110.25 + 196) = √306.25 = 17.5 m. Canvas area = Curved Surface Area = πrl = (22/7) × 10.5 × 17.5 = 577.5 m². Length of canvas = Area / width = 577.5 / 1.1 = 525 m.