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
2841
How many spherical bullets of radius 1 cm can be made out of a solid cube of lead whose edge measures 44 cm? (Use π = 22/7)
Answer:
20328
Volume of cube = 44³ = 85184 cm³. Volume of one bullet = (4/3)πr³ = (4/3) × (22/7) × 1³ = 88/21 cm³. Number of bullets = 85184 / (88/21) = (85184 × 21) / 88 = 968 × 21 = 20328.
2842
A solid cylinder is melted and cast into a sphere of the same radius. What is the ratio of the height to the radius of the original cylinder?
Answer:
4:3
Volume of cylinder = Volume of sphere. πr²h = (4/3)πr³. Dividing both sides by πr² gives h = (4/3)r. Thus, the ratio of height to radius (h/r) is 4/3 or 4:3.
2843
The areas of three adjacent faces of a cuboid are 15 cm², 20 cm², and 12 cm². What is the volume of the cuboid?
Answer:
60 cm³
Let dimensions be l, w, h. The areas are lw=15, wh=20, lh=12. Volume V = lwh. V² = (lw)(wh)(lh) = 15 × 20 × 12 = 3600. Therefore, V = √3600 = 60 cm³.
2844
What is the surface area of a rectangular prism with length 5 cm, width 4 cm, and height 2 cm?
Answer:
76 cm²
Surface Area = 2(lw + wh + lh) = 2(5×4 + 4×2 + 5×2) = 2(20 + 8 + 10) = 2(38) = 76 cm².
2845
A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform.
Answer:
2.5 m
Volume of earth dug out = Volume of well (cylinder) = πr²h = (22/7) × (3.5)² × 20 = (22/7) × 12.25 × 20 = 770 m³. Volume of platform = length × width × height = 22 × 14 × h. So, 308h = 770, giving h = 770 / 308 = 2.5 m.
2846
If the perimeters of the base of two cylinders are in the ratio 3:4 and their heights are in the ratio 4:5, what is the ratio of their lateral surface areas?
Answer:
3:5
Lateral surface area = Perimeter of base × height. Let the perimeters be 3P and 4P, and heights be 4H and 5H. Area ratio = (3P × 4H) : (4P × 5H) = 12 : 20 = 3 : 5.
2847
A right triangle with sides 3 cm, 4 cm, and 5 cm is revolved about the 4 cm side to form a cone. What is the volume of the cone generated?
Answer:
12π cm³
When revolved about the 4 cm side, the height of the cone becomes 4 cm, and the base radius becomes 3 cm. Volume = (1/3)πr²h = (1/3)π(3)²(4) = (1/3)π(9)(4) = 12π cm³.
2848
A cone of height 24 cm and base radius 6 cm is made up of modeling clay. A child reshapes it into a sphere. Find the radius of the sphere.
Answer:
6 cm
Volume of cone = (1/3)π(6)²(24) = 288π. Volume of sphere = (4/3)πr³. Since volumes are equal, (4/3)πr³ = 288π. r³ = (288 × 3) / 4 = 72 × 3 = 216. Therefore, r = 6 cm.
2849
Find the ratio of the volume of a cube to the volume of the largest sphere that can fit perfectly inside it.
Answer:
6 : π
Let the side of the cube be a. Volume of cube = a³. The largest sphere has a diameter equal to a, so radius r = a/2. Volume of sphere = (4/3)π(a/2)³ = (4/3)π(a³/8) = πa³/6. Ratio = a³ : (πa³/6) = 1 : (π/6) = 6 : π.
2850
If the diameter of a sphere is decreased by 25%, by what percent does its curved surface area decrease?
Answer:
43.75%
Surface area is proportional to the square of the diameter. If the new diameter is 75% (0.75) of the original, the new area is (0.75)² = 0.5625 of the original area. The decrease is 1 - 0.5625 = 0.4375, which is 43.75%.