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
2941
What is the ratio of the total surface area to the curved surface area of a cylinder with radius 5 cm and height 15 cm?
Answer:
4:3
Step 1: TSA = 2πr(r+h) and CSA = 2πrh. Step 2: Ratio = [2πr(r+h)] / [2πrh] = (r+h) / h. Step 3: Substitute values: (5+15) / 15 = 20 / 15 = 4:3.
2942
The total surface area of a solid right circular cylinder is 1540 cm². If its height is 4 times its base radius, find the radius.
Answer:
7 cm
Step 1: TSA = 2πr(r+h). Given h = 4r. Step 2: 2πr(r + 4r) = 2πr(5r) = 10πr² = 1540. Step 3: 10 × (22/7) × r² = 1540 -> (220/7)r² = 1540 -> r² = 49 -> r = 7 cm.
2943
A cylindrical tank has a capacity of 6160 m³. If the diameter of its base is 28 m, find its depth.
Answer:
10 m
Step 1: Radius = 14 m. Volume = πr²h. Step 2: 6160 = (22/7) × 14² × h = 22 × 28 × h = 616h. Step 3: h = 6160 / 616 = 10 m.
2944
Find the ratio of the volume of a cube to that of a sphere which will fit exactly inside the cube.
Answer:
6 : π
Step 1: Let the edge of the cube be a. The diameter of the sphere is 'a', so radius r = a/2. Step 2: Vol of cube = a³. Vol of sphere = (4/3)π(a/2)³ = (4/3)π(a³/8) = πa³/6. Step 3: Ratio = a³ : (πa³/6) = 1 : π/6 = 6 : π.
2945
Three identical cubes of edge 4 cm are joined end to end. Find the total surface area of the resulting cuboid.
Answer:
224 cm²
Step 1: The new cuboid has dimensions l = 12, b = 4, h = 4. Step 2: TSA = 2(lb + bh + hl) = 2(12×4 + 4×4 + 4×12). Step 3: TSA = 2(48 + 16 + 48) = 2(112) = 224 cm².
2946
A right circular cone of radius 3 cm has a curved surface area of 47.1 cm². Find the volume of the cone. (Take π = 3.14)
Answer:
37.68 cm³
Step 1: CSA = πrl = 47.1. So 3.14 × 3 × l = 47.1 -> 9.42l = 47.1 -> l = 5 cm. Step 2: h = √(l² - r²) = √(25 - 9) = 4 cm. Step 3: Volume = (1/3)πr²h = (1/3) × 3.14 × 9 × 4 = 37.68 cm³.
2947
A rectangular water tank is 5 m long, 3 m wide, and 2 m deep. How many liters of water can it hold?
Answer:
30,000 L
Step 1: Volume = 5 × 3 × 2 = 30 m³. Step 2: 1 m³ = 1000 Liters. Step 3: Capacity = 30 × 1000 = 30,000 Liters.
2948
If the volume of a cuboid is 144 cm³ and its base area is 24 cm², what is its height?
Answer:
6 cm
Step 1: Volume of a cuboid = Base Area × Height. Step 2: 144 = 24 × Height. Step 3: Height = 144 / 24 = 6 cm.
2949
If the circumference of the base of a cylinder is 44 cm and its height is 10 cm, find its lateral surface area.
Answer:
440 cm²
Step 1: Circumference = 2πr = 44. Step 2: Lateral surface area (CSA) = 2πrh. Step 3: CSA = 44 × 10 = 440 cm².
2950
A cone and a hemisphere have the same base and same volume. Find the ratio of their heights.
Answer:
2:1
Step 1: Vol of cone = (1/3)πr²h. Vol of hemisphere = (2/3)πr³. Step 2: Since volumes are equal, (1/3)πr²h = (2/3)πr³. Step 3: This simplifies to h = 2r. The height of the hemisphere is r. So ratio is 2r : r = 2:1.