MCQ
Mensuration: area, perimeter and volume MCQ - Practice Questions with Answers
Solve 10 Mensuration: area, perimeter and volume questions for RAS/RPSC preparation.
Practice questions
Q1A rectangular sports ground is 80 m long and 50 m broad. If fencing is required around the ground but a 5 m gate is left open, how much fencing is needed?
A fencing question asks for the boundary length, so the rectangle perimeter formula is used: 2 x (length + breadth). For 80 m and 50 m, the full boundary is 2 x (80 + 50) = 260 m. The story may require subtracting an opening such as a gate. Since a 5 m gate is left open, that part does not need fencing. Required fencing is therefore 260 - 5 = 255 m.
Q2A circular garden has diameter 14 m. Using pi = 22/7, what is its area?
For a circle, There are area = pi x r^2. When diameter is given, the radius must first be found by dividing the diameter by 2. A diameter of 14 m gives radius 7 m. Using pi = 22/7, the area is 22/7 x 7 x 7 = 154 m^2. The value 44 m is the circumference, while using 14 as the radius would wrongly make the area four times larger.
Q3Which statement about the area of a triangle is correct?
The area of a triangle is 1/2 x base x height. They also stress that the height must be perpendicular to the chosen base; a slant side should not be treated as height. Therefore the correct rule combines both points: take half of the product of the base and the perpendicular height. The sum of sides belongs to perimeter, while base x height without the half factor belongs to a rectangle-style calculation, not a triangle.
Q4Match the situation with the measure required. List I: 1. Filling a rectangular tank 2. Painting only the four side walls of a room 3. Covering the outside curved part of a pipe List II: a. Curved surface area of a cylinder b. Lateral surface area of a cuboid c. Volume of a cuboid
Measurement differ by wording. Filling a rectangular tank asks for the space inside it, so it needs the volume of a cuboid. Painting only the four side walls of a room means lateral surface area of a cuboid, not total surface area or volume. Covering the outside curved part of a pipe uses the curved surface area of a cylinder. This gives the matching: tank filling with cuboid volume, four walls with cuboid lateral surface area, and pipe surface with cylinder curved surface area.
Q5Consider the statements about scaling. Statement 1: If every side of a square is doubled, its perimeter becomes double. Statement 2: If every edge of a cube is doubled, its volume becomes eight times. Which of the following is correct?
Perimeter depends on one dimension, area on two dimensions and volume on three dimensions. When every side of a square is doubled, the square perimeter also doubles because perimeter is a boundary length. For a cube, doubling every edge multiplies volume by 2 x 2 x 2, which is 8. Therefore the statement about square perimeter and the statement about cube volume are both correct.
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More questions
6Match List I with List II. List I: 1. Radius of a circle 2. Diameter of a circle 3. Area of a semicircle 4. Perimeter of a semicircle List II: a. Half of the full circle area b. Distance from centre to boundary c. pi x radius + 2 x radius d. Twice the radius
7A rectangular field is 80 m long and 50 m broad. A 5 m gate is left unfenced, and three rounds of wire are used around the remaining boundary. How much wire is required?
8In a mensuration question, which unit clue most directly shows that the examiner is asking for area, not perimeter or volume?
9Read the assertion and reason. Assertion (A): For applying material on the complete outside of a closed cylindrical tin, total surface area is required. Reason (R): Total surface area of a cylinder includes the curved surface and the two circular ends. Choose the correct answer.
10Read the statements and choose the correct combination. Statement 1: 1 square metre = 10,000 square centimetres. Statement 2: 1 cubic metre = 10,000 cubic centimetres. Statement 3: 1 cubic metre = 1000 litres.