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
2791
The volume of a regular triangular prism is 120√3 cm³. If its height is 10 cm, find the side length of its base.
Answer:
4√3 cm
Volume = Base Area × height. Base Area = 120√3 / 10 = 12√3 cm². Since the base is an equilateral triangle, Area = (√3/4)s² = 12√3. Dividing by √3 gives s²/4 = 12, so s² = 48. Therefore, side s = √48 = 4√3 cm.
2792
A wire in the shape of a rectangle of length 18 cm and width 15 cm is bent to form a circle. What is the radius of the circle? (Use π = 22/7)
Answer:
10.5 cm
Perimeter of rectangle = length of wire = 2(18 + 15) = 2(33) = 66 cm. This wire forms a circle, so Circumference = 66 cm. 2πr = 66 => 2 × (22/7) × r = 66 => (44/7)r = 66 => r = (66 × 7) / 44 = 3 × 7 / 2 = 21 / 2 = 10.5 cm.
2793
If the radius of a cone is doubled and the height is tripled, what is the ratio of the new volume to the original volume?
Answer:
12:1
Original Volume = (1/3)πr²h. New Volume = (1/3)π(2r)²(3h) = (1/3)π(4r²)(3h) = 12 × (1/3)πr²h. The new volume is 12 times the original, so the ratio is 12:1.
2794
If the surface area of a cube is numerically equal to its volume, what is the length of its edge?
Answer:
6 units
Surface Area = 6s², Volume = s³. Given 6s² = s³. Since an edge length cannot be zero, divide by s² to get s = 6 units.
2795
A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by:
Answer:
2.25 cm
Volume of water displaced = Volume of sphere = (4/3)π(3³) = 36π cm³. This volume forms a cylinder of water in the vessel with radius 4 cm and height h. So, π(4²)h = 36π => 16h = 36 => h = 36 / 16 = 2.25 cm.
2796
The dimensions of a brick are 24 cm × 12 cm × 8 cm. How many bricks will be required to build a wall 24 m long, 8 m high, and 60 cm thick, if 10% of the wall is filled with mortar?
Answer:
45,000
Volume of wall = 2400 cm × 800 cm × 60 cm = 115,200,000 cm³. Since 10% is mortar, 90% is bricks. Volume of bricks = 0.9 × 115,200,000 = 103,680,000 cm³. Volume of one brick = 24 × 12 × 8 = 2304 cm³. Number of bricks = 103,680,000 / 2304 = 45,000.
2797
What is the total surface area of a pyramid whose base is a square with side 8 cm and whose slant height is 10 cm?
Answer:
224 cm²
Total Surface Area = Base Area + Lateral Surface Area. Base Area = 8 × 8 = 64 cm². Lateral Area consists of 4 triangles = 4 × (1/2 × base × slant_height) = 4 × (1/2 × 8 × 10) = 4 × 40 = 160 cm². TSA = 64 + 160 = 224 cm².
2798
A hemispherical bowl is made of steel 0.5 cm thick. The inside radius of the bowl is 4 cm. Find the volume of the steel used in making the bowl. (Use π ≈ 3.14, approx to nearest whole number)
Answer:
57 cm³
Internal radius r = 4 cm. External radius R = 4 + 0.5 = 4.5 cm. Volume of steel = (2/3)π(R³ - r³) = (2/3) × 3.14 × (4.5³ - 4³) = (2/3) × 3.14 × (91.125 - 64) = 2.093 × 27.125 ≈ 56.78 cm³. The closest whole number is 57 cm³.
2799
If the radius of a cylinder is decreased by 50% and its height is increased by 50%, what is the net percentage change in its volume?
Answer:
62.5% decrease
Original Volume V = πr²h. New radius = 0.5r. New height = 1.5h. New Volume V' = π(0.5r)²(1.5h) = π(0.25r²)(1.5h) = 0.375πr²h = 0.375V. The new volume is 37.5% of the original. The decrease is 100% - 37.5% = 62.5%.
2800
A tank is 5 m long, 4 m wide, and 3 m deep. How much will it cost to plaster its walls and bottom at the rate of Rs. 20 per m²?
Answer:
Rs. 1480
Area to be plastered = Area of 4 walls + Area of bottom = 2h(l + w) + lw. Area = 2 × 3 × (5 + 4) + (5 × 4) = 6 × 9 + 20 = 54 + 20 = 74 m². Cost = 74 × 20 = Rs. 1480.