Questions 226–234 of 234 Geometry and Mensuration MCQs — start at page 1 for an overview.
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Geometry and Mensuration
The length and breadth of a rectangle are in the ratio 5:4. Find its perimeter if its area is 180 cm².
Correct answer: A
Let the length and breadth be 5x and 4x respectively. Area = length × breadth = 5x × 4x = 20x² = 180, so x² = 9 and x = 3. Therefore, length = 15 cm and breadth = 12 cm. Perimeter = 2 × (length + breadth) = 2 × (15 + 12) = 54 cm.
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Geometry and Mensuration
The plan for a rectangular area is drawn to a scale of 1:500. If the length and breadth in the plan are 30 cm and 20 cm respectively, find the actual area.
Correct answer: D
The scale 1:500 means 1 cm on the plan represents 500 cm (or 5 m) in actual length. The actual length is 30 cm × 5 m/cm = 150 m, and the actual breadth is 20 cm × 5 m/cm = 100 m. Therefore, the actual area = 150 m × 100 m = 15,000 m², which corresponds to option D.
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Geometry and Mensuration
A dealer professing to sell at cost price uses a 900 g weight for a kilogram. His gain percent is: ______?
Correct answer: D
The dealer uses 900 g instead of 1000 g but charges for 1000 g, so gain = (1000 - 900)/900 × 100% = 100/900 × 100% = 11 1/9%.
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Geometry and Mensuration
The angle of elevation of a ladder leaning against a wall is 60°, and the foot of the ladder is 4.6 m away from the wall. What is the length of the ladder?
Correct answer: D
The ladder forms a right triangle with the wall and the ground. The angle of elevation is 60°, and the foot of the ladder is 4.6 m from the wall, which is the adjacent side to the angle. Using the cosine function: cos(60°) = adjacent/hypotenuse = 4.6 / ladder length. Since cos(60°) = 0.5, ladder length = 4.6 / 0.5 = 9.2 m. Therefore, the length of the ladder is 9.2 meters, which corresponds to option D.
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Geometry and Mensuration
The word 'Geometry' has been derived from two Greek words: ________?
Correct answer: D
The word 'Geometry' is derived from the Greek words 'Geo' meaning 'Earth' and 'Metron' meaning 'Measurement', so 'Geometry' literally means 'Earth measurement'.
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Geometry and Mensuration
Coordinates of the origin are: ________?
Correct answer: C
The origin in a coordinate system is the point where the x-axis and y-axis intersect, which is at (0,0). This is the standard definition in coordinate geometry.
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Geometry and Mensuration
Choose the analogous pair: Cube : Cuboid
Correct answer: B
The analogy Cube : Cuboid relates a three-dimensional shape to another three-dimensional shape where the first is a special case of the second (a cube is a special type of cuboid). Similarly, Square : Cube relates a two-dimensional shape to a three-dimensional shape where the first is the base shape of the second (a square is the base of a cube). Option C (Sphere : Ellipsoid) relates two 3D shapes but neither is a special case of the other in the same way. Therefore, option B is the best analogous pair.
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Geometry and Mensuration
Who is known as the Father of Geometry?
Correct answer: B
Euclid is known as the Father of Geometry because of his foundational work 'Elements,' which systematically organized the principles of geometry.
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Geometry and Mensuration
A right-angled prism has how many faces?
Correct answer: C
A right-angled prism, commonly known as a rectangular prism or cuboid, has 6 faces. These include the top, bottom, front, back, and two side faces.
