MCQ
Numerical: Mensuration 3D MCQ - Practice Questions with Answers
Solve 10 Numerical: Mensuration 3D questions for RAS/RPSC preparation.
Practice questions
Q1Match each solid with its volume. Use π = 22/7 for the cylinder. 1. Cube of side 6 cm; 2. Cuboid of length 10 cm, breadth 6 cm and height 4 cm; 3. Cylinder of radius 7 cm and height 5 cm.
Compute each volume separately. For the cube, volume = a³ = 6³ = 216 cm³. For the cuboid, volume = lbh = 10 × 6 × 4 = 240 cm³. For the cylinder, volume = πr²h = (22/7) × 7² × 5 = (22/7) × 49 × 5 = 770 cm³. Therefore the correct matching is 1 - 216 cm³, 2 - 240 cm³ and 3 - 770 cm³.
Q2For a cuboid of length 10 cm, breadth 6 cm and height 4 cm, consider these statements: 1. Volume = 240 cm³. 2. Total surface area = 248 cm². 3. Lateral surface area = 128 cm². Which statements are correct?
Check each statement. Volume of a cuboid = lbh = 10 × 6 × 4 = 240 cm³, so statement 1 is correct. Total surface area = 2(lb + bh + lh) = 2(10 × 6 + 6 × 4 + 10 × 4) = 2(60 + 24 + 40) = 248 cm², so statement 2 is correct. Lateral surface area = 2h(l + b) = 2 × 4 × (10 + 6) = 128 cm², so statement 3 is also correct.
Q3Fill in the blank: The volume of a cylinder with radius 7 cm and height 10 cm is _____. Use π = 22/7.
The volume of a cylinder is πr²h. Here, r = 7 cm, h = 10 cm, and π = 22/7. Volume = (22/7) × 7² × 10 = (22/7) × 49 × 10. Cancelling 7 from 49 gives 7, so the value is 22 × 7 × 10 = 1540 cm³. Therefore, the blank should be filled with 1540 cm³.
Q4A cuboid has length 10 cm, breadth 6 cm and height 4 cm. Which statement is correct?
For a cuboid, total surface area = 2(lb + bh + lh). Here, l = 10 cm, b = 6 cm and h = 4 cm. So lb = 60, bh = 24 and lh = 40. Their sum is 60 + 24 + 40 = 124. Total surface area = 2 × 124 = 248 cm². The statement saying that the total surface area is 248 cm² is correct.
Q5Match each solid with the given measure. Use π = 22/7 where needed. 1. Cube of edge 4 cm: volume; 2. Sphere of radius 7 cm: surface area; 3. Cylinder of radius 3 cm and height 14 cm: volume.
Compute the required measure for each solid. For the cube, volume = a³ = 4³ = 64 cm³. For the sphere, surface area = 4πr² = 4 × (22/7) × 7 × 7 = 616 cm². For the cylinder, volume = πr²h = (22/7) × 3 × 3 × 14. Since 14 ÷ 7 = 2, this becomes 22 × 9 × 2 = 396 cm³. Hence the correct matching is 1-64 cm³, 2-616 cm² and 3-396 cm³.
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More questions
6A cube has an edge of 9 cm. What is its volume?
7The side of a cube is 9 cm. What is its total surface area?
8For a cone with radius 7 cm and height 24 cm, use π = 22/7. Which statement is incorrect?
9The radius of a cone is 7 cm and its height is 15 cm. Using π = 22/7, find its volume.
10A closed cylinder has radius 7 cm and height 8 cm. Using π = 22/7, which statement about its total surface area is correct?