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
2911
The volume of a right circular cone is 100π cm³, and its height is 12 cm. Find its slant height.
Answer:
13 cm
Step 1: Volume = (1/3)πr²h = 100π. So, (1/3)r²(12) = 100 -> 4r² = 100 -> r² = 25 -> r = 5 cm. Step 2: Slant height l = √(r² + h²). Step 3: l = √(5² + 12²) = √(25 + 144) = √169 = 13 cm.
2912
If a solid sphere of radius 10 cm is melted and recast into small spheres of radius 2 cm each, how many small spheres can be formed?
Answer:
125
Step 1: Number of spheres = Volume of large sphere / Volume of small sphere. Step 2: Since volume is proportional to r³, the ratio is (R/r)³. Step 3: (10/2)³ = 5³ = 125.
2913
A cylindrical tank is 14 m in radius and 30 m deep. What is the area of its total closed surface?
Answer:
3872 m²
Step 1: TSA = 2πr(r+h). Step 2: TSA = 2 × (22/7) × 14 × (14 + 30). Step 3: TSA = 88 × 44 = 3872 m².
2914
The radii of two right circular cylinders are in the ratio of 2:3 and their heights are in the ratio of 5:4. The ratio of their curved surface areas is:
Answer:
5:6
Step 1: CSA = 2πrh. Step 2: Ratio = (r1 × h1) / (r2 × h2) = (2 × 5) / (3 × 4). Step 3: Ratio = 10 / 12 = 5:6.
2915
A cuboidal block of 6 cm × 9 cm × 12 cm is cut up into an exact number of equal cubes. The least possible number of cubes will be:
Answer:
24
Step 1: Find the HCF of the dimensions (6, 9, 12) to get the largest possible side length of the cube, which minimizes the number of cubes. HCF = 3 cm. Step 2: Volume of block = 6 × 9 × 12 = 648 cm³. Volume of cube = 3³ = 27 cm³. Step 3: Number of cubes = 648 / 27 = 24.
2916
If a hemisphere is melted and recast into a cylinder of the same radius, find the ratio of the height of the cylinder to its radius.
Answer:
2:3
Step 1: Vol of hemisphere = Vol of cylinder. (2/3)πr³ = πr²h. Step 2: Divide both sides by πr²: (2/3)r = h. Step 3: Ratio h:r = 2:3.
2917
What is the slant height of a cone whose volume is 12936 cm³ and base diameter is 42 cm? (Take π = 22/7)
Answer:
35 cm
Step 1: Radius = 21 cm. Volume = (1/3)πr²h = 12936. Step 2: (1/3) × (22/7) × 441 × h = 12936 -> 462h = 12936 -> h = 28 cm. Step 3: Slant height l = √(r² + h²) = √(21² + 28²) = √(441 + 784) = √1225 = 35 cm.
2918
If the surface area of a sphere is 346.5 m², what is its radius? (Take π = 22/7)
Answer:
5.25 m
Step 1: SA = 4πr² = 346.5. Step 2: 4 × (22/7) × r² = 346.5 -> (88/7)r² = 346.5. Step 3: r² = (346.5 × 7) / 88 = 2425.5 / 88 = 27.5625. r = √27.5625 = 5.25 m.
2919
A right circular cylinder and a right circular cone have the same radius and same height. The ratio of their curved surface areas is 8:5. What is the ratio of their radius to their height?
Answer:
3:4
Step 1: Ratio = 2πrh / πr√(r²+h²) = 8/5. So 2h / √(r²+h²) = 8/5 -> h / √(r²+h²) = 4/5. Step 2: Square both sides: h² / (r² + h²) = 16/25. Step 3: 25h² = 16r² + 16h² -> 9h² = 16r² -> r²/h² = 9/16 -> r:h = 3:4.
2920
The dimensions of a room are 10 m, 8 m, and 3.3 m. How many persons can be accommodated if each person requires 3 cubic meters of space?
Answer:
88
Step 1: Find the volume of the room: V = 10 × 8 × 3.3 = 264 m³. Step 2: Each person needs 3 m³. Step 3: Number of persons = 264 / 3 = 88.