Numerical: Mensuration 3D — Cube, Cuboid & Cylinder MCQ — 15 Practice Questions with Answers

Explanation

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.

Explanation

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.

Explanation

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.

Explanation

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.

Explanation

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.