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
3141
Find the total surface area of a cuboid measuring 10 cm by 6 cm by 5 cm.
Answer:
280 cm²
The total surface area of a cuboid is 2(lw + wh + hl). Substituting the values: 2 * (10*6 + 6*5 + 5*10) = 2 * (60 + 30 + 50) = 2 * 140 = 280 cm².
3142
What is the volume of a cuboid with dimensions length = 8 cm, width = 5 cm, and height = 4 cm?
Answer:
160 cm³
The volume of a cuboid is calculated as Volume = length * width * height. Substituting the given values: Volume = 8 * 5 * 4 = 160 cm³.
3143
If the total surface area of a cube is 150 cm², find its volume.
Answer:
125 cm³
Total Surface Area = 6 * side² = 150. Solving for side: side² = 150 / 6 = 25, which means side = 5 cm. The volume is side³ = 5³ = 125 cm³.
3144
If the volume of a cube is 512 cm³, what is the length of its side?
Answer:
8 cm
The volume of a cube is V = side³. We know V = 512 cm³. To find the side, we take the cube root of 512. The cube root of 512 is 8, so the side length is 8 cm.
3145
What is the length of the main diagonal of a cube with side length 'a'?
Answer:
a√3
The length of the main space diagonal of a cube that connects two opposite corners through the center is calculated using the 3D Pythagorean theorem: Diagonal = √(a² + a² + a²) = √(3a²) = a√3.
3146
Find the total surface area of a cube with an edge of 4 cm.
Answer:
96 cm²
A cube has 6 identical square faces. The total surface area is 6 * side². Substituting the side length of 4 cm: Total Surface Area = 6 * (4²) = 6 * 16 = 96 cm².
3147
What is the volume of a cube with a side length of 5 cm?
Answer:
125 cm³
The volume of a cube is calculated using the formula: Volume = side³. Given the side length is 5 cm, the volume = 5 * 5 * 5 = 125 cm³.
3148
The angle in a semicircle is a:
Answer:
Right angle
According to Thales's theorem, an inscribed angle subtended by a diameter (which creates a semicircle) is always a right angle (90 degrees).
3149
If two circles touch each other externally and their radii are 5 cm and 3 cm, what is the distance between their centers?
Answer:
8 cm
When two circles touch each other externally, the distance between their centers is simply the sum of their radii. Distance = r1 + r2 = 5 cm + 3 cm = 8 cm.
3150
What is the angle subtended by a semicircle at its center?
Answer:
180 degrees
A full circle subtends an angle of 360 degrees at its center. A semicircle is exactly half of a circle, so the angle it subtends at the center is 360 / 2 = 180 degrees (a straight angle).