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
3001
The total surface area of a cube is 96 cm². What is the volume of the cube?
Answer:
64 cm³
Step 1: 6a² = 96, so a² = 16. Step 2: The side of the cube a = 4 cm. Step 3: Volume = a³ = 4³ = 64 cm³.
3002
A right circular cone has a base radius of 7 cm and a height of 24 cm. Find its slant height.
Answer:
25 cm
Step 1: The relationship between slant height (l), radius (r), and height (h) is l = √(r² + h²). Step 2: Substitute values: l = √(7² + 24²). Step 3: l = √(49 + 576) = √625 = 25 cm.
3003
A hemispherical bowl has a radius of 14 cm. What is the capacity of the bowl? (Take π = 22/7)
Answer:
5749.33 cm³
Step 1: Capacity = Volume of hemisphere = (2/3)πr³. Step 2: V = (2/3) × (22/7) × (14)³. Step 3: V = (2/3) × 22 × 2 × 196 = 8624 / 1.5 = 5749.33 cm³.
3004
If the side of a cube is increased by 50%, find the percentage increase in its surface area.
Answer:
125%
Step 1: Let the original side be 10. Initial surface area = 6(10)² = 600. Step 2: New side = 15. New surface area = 6(15)² = 6(225) = 1350. Step 3: Increase = 1350 - 600 = 750. Percentage increase = (750/600) × 100 = 125%.
3005
The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to level a playground. Find the area of the playground in m².
Answer:
1584 m²
Step 1: Area covered in 1 revolution = CSA of roller = 2πrh. r = 42 cm = 0.42 m, h = 1.2 m. Step 2: CSA = 2 × (22/7) × 0.42 × 1.2 = 3.168 m². Step 3: Total area = 500 × 3.168 = 1584 m².
3006
If the radius of a cylinder is doubled and its height is halved, what happens to its volume?
Answer:
Becomes double
Step 1: Original volume V1 = πr²h. Step 2: New radius = 2r, New height = h/2. New volume V2 = π(2r)²(h/2). Step 3: V2 = π(4r²)(h/2) = 2πr²h = 2 × V1. The volume doubles.
3007
A cone and a cylinder have the same base radius and the same height. What is the ratio of their volumes?
Answer:
1:3
Step 1: Vol of cone = (1/3)πr²h. Step 2: Vol of cylinder = πr²h. Step 3: Ratio = [(1/3)πr²h] / [πr²h] = 1/3, or 1:3.
3008
Two cylinders have their radii in the ratio 2:3 and their heights in the ratio 5:3. What is the ratio of their volumes?
Answer:
20:27
Step 1: V1/V2 = (π × r1² × h1) / (π × r2² × h2) = (r1/r2)² × (h1/h2). Step 2: Substitute the given ratios: (2/3)² × (5/3). Step 3: (4/9) × (5/3) = 20/27. So, the ratio is 20:27.
3009
A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and height 3 cm. How many cones are obtained?
Answer:
126
Step 1: Number of cones = Volume of sphere / Volume of one cone. Step 2: Vol of sphere = (4/3)π(10.5)³. Vol of cone = (1/3)π(3.5)²(3). Step 3: Number = [ (4/3)π × 10.5 × 10.5 × 10.5 ] / [ (1/3)π × 3.5 × 3.5 × 3 ] = [4 × 3 × 3 × 10.5] / 3 = 126.
3010
What is the total surface area of a solid hemisphere of radius 7 cm? (Take π = 22/7)
Answer:
462 cm²
Step 1: The total surface area of a solid hemisphere is 3πr². Step 2: Substitute values: TSA = 3 × (22/7) × 7². Step 3: TSA = 3 × 22 × 7 = 462 cm².