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
2881
The volume of a right circular cone with radius 6 cm and height 7 cm is: (Use π = 22/7)
Answer:
264 cm³
The volume of a cone is (1/3)πr²h. V = (1/3) × (22/7) × 6 × 6 × 7 = 22 × 2 × 6 = 264 cm³.
2882
What is the total surface area of a cylinder of radius 7 cm and height 10 cm? (Use π = 22/7)
Answer:
748 cm²
The total surface area of a cylinder is 2πr(r + h). TSA = 2 × (22/7) × 7 × (7 + 10) = 44 × 17 = 748 cm².
2883
Find the curved surface area of a cylinder with radius 14 cm and height 5 cm. (Use π = 22/7)
Answer:
440 cm²
The curved surface area (CSA) of a cylinder is 2πrh. CSA = 2 × (22/7) × 14 × 5 = 2 × 22 × 2 × 5 = 440 cm².
2884
A cylindrical tank has a base radius of 7 m and a height of 10 m. What is its volume? (Use π = 22/7)
Answer:
1540 m³
The volume of a cylinder is πr²h. Substituting the values: V = (22/7) × (7)² × 10 = 22 × 7 × 10 = 1540 m³.
2885
Find the area of the 4 walls of a room whose length is 10 m, breadth is 8 m, and height is 5 m.
Answer:
180 m²
The area of the 4 walls (Lateral Surface Area) of a cuboid is 2H(L + W). Area = 2 × 5 × (10 + 8) = 10 × 18 = 180 m².
2886
What is the volume of a cuboid with dimensions 10 cm, 8 cm, and 6 cm?
Answer:
480 cm³
The volume of a cuboid is calculated by multiplying its length, width, and height. Volume = L × W × H = 10 × 8 × 6 = 480 cm³.
2887
What is the length of the longest rod that can be placed in a room measuring 12m long, 9m wide, and 8m high?
Answer:
17 m
The longest rod that can be placed in a cuboid is equal to its main diagonal. Diagonal = √(L² + W² + H²) = √(12² + 9² + 8²) = √(144 + 81 + 64) = √289 = 17 m.
2888
Find the total surface area of a cube whose side is 6 cm.
Answer:
216 cm²
The total surface area of a cube is given by 6 × side². For a side of 6 cm, the area is 6 × (6)² = 6 × 36 = 216 cm².
2889
What is the volume of a cube whose side length is 8 cm?
Answer:
512 cm³
The formula for the volume of a cube is V = side³. Given the side length is 8 cm, the volume is 8 × 8 × 8 = 512 cm³.
2890
Find the total surface area of a cone whose radius is r/2 and slant height is 2l.
Answer:
πr(l + r/4)
Step 1: TSA of a cone = πR(R + L). Step 2: Here, R = r/2 and L = 2l. Step 3: TSA = π(r/2)(r/2 + 2l) = πr/2(r/2 + 2l) = πr(r/4 + l) = πr(l + r/4).