MCQ
Numerical: Mensuration 3D — Cube, Cuboid & Cylinder MCQ - Practice Questions with Answers
Solve 15 Numerical: Mensuration 3D — Cube, Cuboid & Cylinder questions for RAS/RPSC preparation.
Practice questions
Q1For a cuboid with length 12 cm, breadth 8 cm and height 5 cm, which of the following statements is correct?
For a cuboid, volume = length × breadth × height. Substituting the given values, volume = 12 × 8 × 5 = 96 × 5 = 480 cm³. The total surface area would be 2(lb + bh + lh) = 2(96 + 40 + 60) = 392 cm², not 312 cm². The lateral surface area is 2h(l + b) = 2 × 5 × 20 = 200 cm². The sum of all edges is 4(l + b + h) = 4 × 25 = 100 cm. Thus, only the volume statement is correct.
Q2The radius of a closed cylindrical tank is 7 cm and its height is 10 cm. Using π = 22/7, find its volume.
The volume of a cylinder is πr²h. Here r = 7 cm and h = 10 cm. Using π = 22/7, volume = (22/7) × 7 × 7 × 10. One 7 cancels with the denominator, so the value becomes 22 × 7 × 10 = 1540. Since volume is measured in cubic units, the volume of the tank is 1540 cm³.
Q3For a cuboid of length 12 centimetres, breadth 8 centimetres and height 5 centimetres, which statement is incorrect? 1. Volume = 480 cubic centimetres 2. Total surface area = 392 square centimetres 3. Lateral surface area = 200 square centimetres 4. Diagonal = 15 centimetres
Check each formula. Volume = lbh = 12 × 8 × 5 = 480 cubic centimetres, so statement 1 is correct. Total surface area = 2(lb + bh + hl) = 2(96 + 40 + 60) = 392 square centimetres, so statement 2 is correct. Lateral surface area = 2(l + b)h = 2(12 + 8) × 5 = 200 square centimetres, so statement 3 is correct. Diagonal = √(12² + 8² + 5²) = √233, not 15. Therefore, statement 4 is incorrect.
Q4A cylinder has radius 7 cm and height 12 cm. Its radius is doubled to 14 cm and its height is halved to 6 cm. Assertion: The new volume is double the original volume. Reason: The volume of a cylinder is directly proportional to r²h. Choose the correct option.
The volume of a cylinder is πr²h. Original volume = (22/7) × 7 × 7 × 12 = 1848 cm³. New volume = (22/7) × 14 × 14 × 6 = 3696 cm³. Now 3696 = 2 × 1848, so the new volume is exactly double the original volume. The reason is also true because cylinder volume depends on r²h. When the radius is doubled and the height is halved, the multiplier is 2² × 1/2 = 2. Hence the reason correctly explains the assertion.
Q5A cylinder has radius 14 cm and height 10 cm. Taking π = 22/7, which of the following statements is incorrect?
For the cylinder, the area of one circular base is πr². With r = 14 cm and π = 22/7, base area = 22/7 × 14 × 14 = 22 × 2 × 14 = 616 cm². The value 1232 cm² is the area of two circular bases, not one base. The other statements check out: volume = 616 × 10 = 6160 cm³, curved surface area = 2πrh = 880 cm², and total surface area = 2πr(h + r) = 2112 cm². Therefore, statement C is incorrect.
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More questions
6A cube has side 9 cm. If all its outer faces are painted at the rate of ₹2 per cm², what will be the total painting cost?
7Match the solid and measurement in List 1 with the correct value in List 2. List 1: 1. Volume of a cube of side 5 centimetres 2. Volume of a cuboid 6 centimetres × 4 centimetres × 3 centimetres 3. Volume of a cylinder with radius 7 centimetres and height 3 centimetres, using π = 22/7 4. Total surface area of a cube of side 6 centimetres
8A cylinder has radius 7 centimetres and height 10 centimetres. Using π = 22/7, find its curved surface area.
9The edge of a cube is 9 cm. Consider these statements: 1. Its volume is 729 cm³. 2. Its total surface area is 486 cm². 3. Its lateral surface area is 243 cm². 4. Its body diagonal is 27 cm. Which statements are correct?
10A cylindrical pipe has radius 7 cm and height 12 cm. Taking π = 22/7, find its curved surface area.
11Match the quantities in List I with the values in List II. List I: P. Volume of a cube of side 6 cm; Q. Total surface area of a cuboid 10 cm × 6 cm × 4 cm; R. Volume of a cylinder of radius 7 cm and height 6 cm; S. Curved surface area of the same cylinder. List II: 1. 248 cm²; 2. 264 cm²; 3. 216 cm³; 4. 924 cm³. Taking π = 22/7, choose the correct matching.
12A rectangular box has length 12 cm, breadth 8 cm and height 5 cm. What is its total surface area?
13A rectangular water tank is 2 metres long, 1.5 metres wide and 1 metre deep. What is its capacity in litres?
14For a cuboid with length 6 cm, breadth 4 cm and height 3 cm, match the quantities with their values: 1. Volume 2. Total surface area 3. Sum of all edge lengths 4. Base area
15The volume of a cube is 512 cubic centimetres. What is its total surface area?