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
3021
If each edge of a cube is doubled, its surface area becomes how many times the original surface area?
Answer:
4 times
Step 1: Original surface area = 6a². Step 2: New edge = 2a, so new surface area = 6(2a)² = 6(4a²) = 24a². Step 3: 24a² is 4 times 6a².
3022
If each edge of a cube is doubled, how many times will its volume become?
Answer:
8 times
Step 1: Let the original edge be 'a', so V1 = a³. Step 2: The new edge is '2a', so the new volume V2 = (2a)³ = 8a³. Step 3: V2 is 8 times the original volume V1.
3023
Three solid cubes of sides 3 cm, 4 cm, and 5 cm are melted to form a new cube. What is the side of the new cube?
Answer:
6 cm
Step 1: Find the total volume of the three cubes: V = 3³ + 4³ + 5³. Step 2: V = 27 + 64 + 125 = 216 cm³. Step 3: The volume of the new cube is 216 cm³, so its side is ³√216 = 6 cm.
3024
What is the total surface area of a cuboid with dimensions 8 cm × 6 cm × 5 cm?
Answer:
236 cm²
Step 1: The total surface area formula is TSA = 2(lb + bh + hl). Step 2: Substitute the values: TSA = 2(8×6 + 6×5 + 5×8). Step 3: TSA = 2(48 + 30 + 40) = 2(118) = 236 cm².
3025
The volume of a cuboid is 320 cm³. If its length and breadth are 10 cm and 8 cm respectively, find its height.
Answer:
4 cm
Step 1: The volume of a cuboid is V = l × b × h. Step 2: Substitute the known values: 320 = 10 × 8 × h. Step 3: Solve for h: 320 = 80h, therefore h = 320 / 80 = 4 cm.
3026
Find the length of the longest pole that can be placed in a room 12 m long, 4 m broad, and 3 m high.
Answer:
13 m
Step 1: The longest pole corresponds to the diagonal of the cuboid. Step 2: The formula is d = √(l² + b² + h²). Step 3: d = √(12² + 4² + 3²) = √(144 + 16 + 9) = √169 = 13 m.
3027
If the surface area of a cube is 150 cm², what is its volume?
Answer:
125 cm³
Step 1: The surface area of a cube is 6a² = 150. Step 2: Solve for a²: a² = 150 / 6 = 25. So, a = 5 cm. Step 3: Calculate the volume: V = a³ = 5³ = 125 cm³.
3028
What is the volume of a cube whose side measures 6 cm?
Answer:
216 cm³
Step 1: The formula for the volume of a cube is V = a³, where 'a' is the side length. Step 2: Substitute a = 6 cm into the formula. Step 3: V = 6 × 6 × 6 = 216 cm³.
3029
If the sides of a triangle are a, b, and c, and s is the semi-perimeter, what does √[s(s-a)(s-b)(s-c)] calculate?
Answer:
Area
This mathematical expression is known as Heron's formula. It is used exclusively to calculate the area of any triangle when the lengths of all three of its sides are known.
3030
What is the sum of the angles in a quadrilateral?
Answer:
360 degrees
A quadrilateral can be split into two triangles by drawing a single diagonal. Since each triangle's interior angles sum to 180 degrees, the quadrilateral's total interior angles sum to 2 * 180 = 360 degrees.