Volume and Surface Area: Formulas, Shortcuts and Solved Examples — MCQs with Answers (Set 7)

Let length = l = 2 m, breadth = b = 10 m, height = h = 11 m. The longest pole that fits equals the room’s space diagonal. Diagonal = sqrt(l^2 + b^2 + h^2). l^2 = 4, b^2 = 100, h^2 = 121. Sum = 4 + 100 + 121 = 225. Diagonal = sqrt(225) = 15 m. Check: 15^2 = 225, which matches the sum above.

Let length = l = 6 m, breadth = b = 9 m, height = h = 18 m. The longest pole that fits equals the room’s space diagonal. Diagonal = sqrt(l^2 + b^2 + h^2). l^2 = 36, b^2 = 81, h^2 = 324. Sum = 36 + 81 + 324 = 441. Diagonal = sqrt(441) = 21 m. Check: 21^2 = 441, which matches the sum above.

Let length = l = 12 m, breadth = b = 18 m, height = h = 36 m. The longest pole that fits equals the room’s space diagonal. Diagonal = sqrt(l^2 + b^2 + h^2). l^2 = 144, b^2 = 324, h^2 = 1296. Sum = 144 + 324 + 1296 = 1764. Diagonal = sqrt(1764) = 42 m. Check: 42^2 = 1764, which matches the sum above.

Let length = l = 4 m, breadth = b = 20 m, height = h = 22 m. The longest pole that fits equals the room’s space diagonal. Diagonal = sqrt(l^2 + b^2 + h^2). l^2 = 16, b^2 = 400, h^2 = 484. Sum = 16 + 400 + 484 = 900. Diagonal = sqrt(900) = 30 m. Check: 30^2 = 900, which matches the sum above.

Let length = l = 25 m, breadth = b = 8 m, height = h = 9 m. Total surface area of a cuboid = 2(lb + bh + lh). lb = 25 x 8 = 200 sq m. bh = 8 x 9 = 72 sq m. lh = 25 x 9 = 225 sq m. Sum = 200 + 72 + 225 = 497 sq m. Surface area = 2 x 497 = 994 sq m.

Let length = l = 9 m, breadth = b = 4 m, height = h = 14 m. Total surface area of a cuboid = 2(lb + bh + lh). lb = 9 x 4 = 36 sq m. bh = 4 x 14 = 56 sq m. lh = 9 x 14 = 126 sq m. Sum = 36 + 56 + 126 = 218 sq m. Surface area = 2 x 218 = 436 sq m.

Let length = l = 7 m, breadth = b = 4 m, height = h = 12 m. Total surface area of a cuboid = 2(lb + bh + lh). lb = 7 x 4 = 28 sq m. bh = 4 x 12 = 48 sq m. lh = 7 x 12 = 84 sq m. Sum = 28 + 48 + 84 = 160 sq m. Surface area = 2 x 160 = 320 sq m.

Let length = l = 17 m, breadth = b = 6 m, height = h = 5 m. Total surface area of a cuboid = 2(lb + bh + lh). lb = 17 x 6 = 102 sq m. bh = 6 x 5 = 30 sq m. lh = 17 x 5 = 85 sq m. Sum = 102 + 30 + 85 = 217 sq m. Surface area = 2 x 217 = 434 sq m.

Let length = l = 26 m, breadth = b = 15 m, height = h = 3 m. Total surface area of a cuboid = 2(lb + bh + lh). lb = 26 x 15 = 390 sq m. bh = 15 x 3 = 45 sq m. lh = 26 x 3 = 78 sq m. Sum = 390 + 45 + 78 = 513 sq m. Surface area = 2 x 513 = 1026 sq m.

Let length = l = 27 m, breadth = b = 24 m, height = h = 15 m. Total surface area of a cuboid = 2(lb + bh + lh). lb = 27 x 24 = 648 sq m. bh = 24 x 15 = 360 sq m. lh = 27 x 15 = 405 sq m. Sum = 648 + 360 + 405 = 1413 sq m. Surface area = 2 x 1413 = 2826 sq m.

Let length = l = 11 m, breadth = b = 9 m, height = h = 15 m. Total surface area of a cuboid = 2(lb + bh + lh). lb = 11 x 9 = 99 sq m. bh = 9 x 15 = 135 sq m. lh = 11 x 15 = 165 sq m. Sum = 99 + 135 + 165 = 399 sq m. Surface area = 2 x 399 = 798 sq m.

Let length = l = 26 m, breadth = b = 22 m, height = h = 3 m. Total surface area of a cuboid = 2(lb + bh + lh). lb = 26 x 22 = 572 sq m. bh = 22 x 3 = 66 sq m. lh = 26 x 3 = 78 sq m. Sum = 572 + 66 + 78 = 716 sq m. Surface area = 2 x 716 = 1432 sq m.

Let length = l = 20 m, breadth = b = 13 m, height = h = 10 m. Total surface area of a cuboid = 2(lb + bh + lh). lb = 20 x 13 = 260 sq m. bh = 13 x 10 = 130 sq m. lh = 20 x 10 = 200 sq m. Sum = 260 + 130 + 200 = 590 sq m. Surface area = 2 x 590 = 1180 sq m.

Let length = l = 12 m, breadth = b = 7 m, height = h = 10 m. Total surface area of a cuboid = 2(lb + bh + lh). lb = 12 x 7 = 84 sq m. bh = 7 x 10 = 70 sq m. lh = 12 x 10 = 120 sq m. Sum = 84 + 70 + 120 = 274 sq m. Surface area = 2 x 274 = 548 sq m.

Let length = l = 8 m, breadth = b = 4 m, height = h = 14 m. Total surface area of a cuboid = 2(lb + bh + lh). lb = 8 x 4 = 32 sq m. bh = 4 x 14 = 56 sq m. lh = 8 x 14 = 112 sq m. Sum = 32 + 56 + 112 = 200 sq m. Surface area = 2 x 200 = 400 sq m.

Let length = l = 26 m, breadth = b = 8 m, height = h = 14 m. Total surface area of a cuboid = 2(lb + bh + lh). lb = 26 x 8 = 208 sq m. bh = 8 x 14 = 112 sq m. lh = 26 x 14 = 364 sq m. Sum = 208 + 112 + 364 = 684 sq m. Surface area = 2 x 684 = 1368 sq m.

Let length = l = 13 m, breadth = b = 5 m, height = h = 13 m. Volume of a cuboid = length x breadth x height. So volume = 13 x 5 x 13. 13 x 5 = 65, and 65 x 13 = 845. So the volume is 845 cubic m.

Let length = l = 21 m, breadth = b = 19 m, height = h = 20 m. Volume of a cuboid = length x breadth x height. So volume = 21 x 19 x 20. 21 x 19 = 399, and 399 x 20 = 7980. So the volume is 7980 cubic m.

Let length = l = 18 m, breadth = b = 4 m, height = h = 12 m. Volume of a cuboid = length x breadth x height. So volume = 18 x 4 x 12. 18 x 4 = 72, and 72 x 12 = 864. So the volume is 864 cubic m.

Let length = l = 7 m, breadth = b = 5 m, height = h = 13 m. Volume of a cuboid = length x breadth x height. So volume = 7 x 5 x 13. 7 x 5 = 35, and 35 x 13 = 455. So the volume is 455 cubic m.

Let length = l = 29 m, breadth = b = 26 m, height = h = 8 m. Volume of a cuboid = length x breadth x height. So volume = 29 x 26 x 8. 29 x 26 = 754, and 754 x 8 = 6032. So the volume is 6032 cubic m.

Let length = l = 14 m, breadth = b = 9 m, height = h = 11 m. Volume of a cuboid = length x breadth x height. So volume = 14 x 9 x 11. 14 x 9 = 126, and 126 x 11 = 1386. So the volume is 1386 cubic m.

Let length = l = 40 m, breadth = b = 18 m, height = h = 7 m. Volume of a cuboid = length x breadth x height. So volume = 40 x 18 x 7. 40 x 18 = 720, and 720 x 7 = 5040. So the volume is 5040 cubic m.

Let length = l = 10 m, breadth = b = 5 m, height = h = 9 m. Volume of a cuboid = length x breadth x height. So volume = 10 x 5 x 9. 10 x 5 = 50, and 50 x 9 = 450. So the volume is 450 cubic m.

Let length = l = 25 m, breadth = b = 6 m, height = h = 13 m. Volume of a cuboid = length x breadth x height. So volume = 25 x 6 x 13. 25 x 6 = 150, and 150 x 13 = 1950. So the volume is 1950 cubic m.

Let length = l = 17 m, breadth = b = 7 m, height = h = 7 m. Volume of a cuboid = length x breadth x height. So volume = 17 x 7 x 7. 17 x 7 = 119, and 119 x 7 = 833. So the volume is 833 cubic m.

Let length = l = 19 m, breadth = b = 18 m, height = h = 14 m. Volume of a cuboid = length x breadth x height. So volume = 19 x 18 x 14. 19 x 18 = 342, and 342 x 14 = 4788. So the volume is 4788 cubic m.

Let length = l = 19 m, breadth = b = 18 m, height = h = 14 m. Volume of a cuboid = length x breadth x height. So volume = 19 x 18 x 14. 19 x 18 = 342, and 342 x 14 = 4788. So the volume is 4788 cubic m.

Let length = l = 9 m, breadth = b = 6 m, height = h = 3 m. Volume of a cuboid = length x breadth x height. So volume = 9 x 6 x 3. 9 x 6 = 54, and 54 x 3 = 162. So the volume is 162 cubic m.

Let length = l = 14 m, breadth = b = 8 m, height = h = 20 m. Volume of a cuboid = length x breadth x height. So volume = 14 x 8 x 20. 14 x 8 = 112, and 112 x 20 = 2240. So the volume is 2240 cubic m.

Let length = l = 14 m, breadth = b = 8 m, height = h = 20 m. Volume of a cuboid = length x breadth x height. So volume = 14 x 8 x 20. 14 x 8 = 112, and 112 x 20 = 2240. So the volume is 2240 cubic m.

Let length = l = 36 m, breadth = b = 35 m, height = h = 7 m. Volume of a cuboid = length x breadth x height. So volume = 36 x 35 x 7. 36 x 35 = 1260, and 1260 x 7 = 8820. So the volume is 8820 cubic m.