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
3081
If the diagonals of a rhombus are equal, then the rhombus must be a:
Answer:
Square
A rhombus inherently has four equal sides. If its diagonals are also equal, then all its interior angles must be 90 degrees. A rhombus with 90-degree angles is a square.
3082
Find the lateral surface area of a regular square pyramid with a base side of 10 cm and a slant height of 12 cm.
Answer:
240 cm²
A square pyramid has 4 identical triangular faces making up its lateral surface. The area of one triangle is (1/2) * base * slant_height = (1/2) * 10 * 12 = 60 cm². For 4 faces, the total lateral surface area is 4 * 60 = 240 cm².
3083
If two sides of a triangle are 8 and 14, which of the following cannot be the length of the third side?
Answer:
22
By the Triangle Inequality Theorem, the third side (x) must be greater than the difference and less than the sum of the other two sides. 14 - 8 < x < 14 + 8, meaning 6 < x < 22. Thus, the third side cannot be 22 or larger.
3084
The areas of three adjacent faces of a cuboid are x, y, and z. What is the volume of the cuboid in terms of x, y, and z?
Answer:
√(xyz)
Let the dimensions of the cuboid be l, w, and h. The areas are x = lw, y = wh, and z = hl. Multiplying these gives x*y*z = (lw)(wh)(hl) = l²w²h² = (lwh)². Since Volume V = lwh, we have V² = xyz. Therefore, V = √(xyz).
3085
In a regular polygon, each interior angle is 144 degrees. How many sides does the polygon have?
Answer:
10
If the interior angle is 144 degrees, the exterior angle is 180 - 144 = 36 degrees. The number of sides in a regular polygon is 360 / exterior angle. Thus, 360 / 36 = 10 sides.
3086
A rectangular solid has sides of 3 cm, 4 cm, and 5 cm. What is the length of the diagonal across the rectangular solid?
Answer:
5√2 cm
The diagonal of a cuboid is √(l² + w² + h²). Substituting the values: √(3² + 4² + 5²) = √(9 + 16 + 25) = √50 = √(25 * 2) = 5√2 cm.
3087
What is the volume of a right prism if its base is an equilateral triangle of side 4 cm, and its length is 10 cm?
Answer:
40√3 cm³
Volume of a prism = Base Area * length. The base is an equilateral triangle with area = (√3 / 4) * side² = (√3 / 4) * 4² = 4√3 cm². Volume = 4√3 * 10 = 40√3 cm³.
3088
Find the sum of the interior angles of a dodecagon (12-sided polygon).
Answer:
1800 degrees
The formula for the sum of interior angles is (n - 2) * 180. For a dodecagon, n = 12. Sum = (12 - 2) * 180 = 10 * 180 = 1800 degrees.
3089
A solid metal cube with an edge of 10 cm is melted and recast into a sphere. What is the volume of the sphere?
Answer:
1000 cm³
When a solid object is melted and recast into another shape, its volume remains completely unchanged. The volume of the cube is 10³ = 1000 cm³, so the volume of the new sphere is also exactly 1000 cm³.
3090
If the length of a rectangle increases by 20% and the width increases by 30%, what is the percentage increase in area?
Answer:
56%
Let original length be L and width be W. Area = LW. New length = 1.2L, new width = 1.3W. New Area = (1.2L) * (1.3W) = 1.56LW. This represents a 56% increase over the original area.