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
3041
What is the volume of a right triangular prism if the base is an equilateral triangle with side 6 cm, and the length of the prism is 10 cm?
Answer:
90√3 cm³
Volume = Base Area * length. Base Area of equilateral triangle = (√3/4) * side² = (√3/4) * 36 = 9√3 cm². Volume = 9√3 * 10 = 90√3 cm³.
3042
If a cone is cut by a plane parallel to its base, the lower part of the solid formed is called a:
Answer:
Frustum
When a cone is sliced by a plane parallel to its circular base, the tip forms a smaller cone, and the remaining bottom portion is geometrically defined as a frustum of a cone.
3043
What is the total surface area of a hemisphere with a radius of 10 cm? (Use π ≈ 3.14)
Answer:
942 cm²
The total surface area of a solid hemisphere is 3πr². Substituting the values: TSA = 3 * 3.14 * 10² = 3 * 3.14 * 100 = 3 * 314 = 942 cm².
3044
A room is 10 m long, 8 m wide, and 3 m high. What is the area of its four walls?
Answer:
108 m²
The area of four walls (Lateral Surface Area) is calculated as 2h(l + w). Substituting the values: Area = 2 * 3 * (10 + 8) = 6 * 18 = 108 m².
3045
What is the relation between the number of edges (E), faces (F), and vertices (V) of a cube?
Answer:
F = 6, V = 8, E = 12
A standard cube has 6 square faces, 8 corner vertices, and 12 edges. This perfectly satisfies Euler's formula: 6 + 8 = 12 + 2.
3046
A cylindrical tank has a radius of 5 m and a height of 10 m. What is its capacity in liters? (Use π ≈ 3.14)
Answer:
785,000 liters
Volume = πr²h = 3.14 * 5² * 10 = 3.14 * 25 * 10 = 785 m³. Since 1 m³ is equivalent to 1000 liters, the capacity is 785 * 1000 = 785,000 liters.
3047
The volume of a sphere is numerically equal to its surface area. What is its radius?
Answer:
3 units
Set the volume formula equal to the surface area formula: (4/3)πr³ = 4πr². Dividing both sides by 4πr² leaves r/3 = 1, which means r = 3 units.
3048
What is the circumcenter of a right-angled triangle located?
Answer:
At the midpoint of the hypotenuse
For any right-angled triangle, the circumcenter (the center of the circle that passes through all three vertices) lies exactly at the midpoint of the hypotenuse.
3049
The point of intersection of the altitudes of a triangle is called the:
Answer:
Orthocenter
In geometry, the point where all three altitudes of a triangle intersect is specifically known as the orthocenter.
3050
Which set of side lengths can form a valid triangle?
Answer:
5, 6, 10
According to the Triangle Inequality Theorem, the sum of the lengths of any two sides must be strictly greater than the length of the third side. In option C: 5+6>10, 6+10>5, and 5+10>6. All conditions are satisfied.