Volume and Surface Area: Formulas, Shortcuts and Solved Examples — MCQs with Answers (Set 6)

Let the edge of the cube = a, with volume = 729 cubic cm. Volume of a cube = a^3, so a = cube root of the volume. a = cube root of 729 = 9 cm. Check: 9^3 = 9 x 9 x 9 = 729, which matches 729.

Let the edge of the cube = a, with volume = 2197 cubic cm. Volume of a cube = a^3, so a = cube root of the volume. a = cube root of 2197 = 13 cm. Check: 13^3 = 13 x 13 x 13 = 2197, which matches 2197.

Let the edge of the cube = a, with volume = 216 cubic cm. Volume of a cube = a^3, so a = cube root of the volume. a = cube root of 216 = 6 cm. Check: 6^3 = 6 x 6 x 6 = 216, which matches 216.

Let the edge of the cube = a, with volume = 1331 cubic cm. Volume of a cube = a^3, so a = cube root of the volume. a = cube root of 1331 = 11 cm. Check: 11^3 = 11 x 11 x 11 = 1331, which matches 1331.

Let the edge of the cube = a, with volume = 8000 cubic cm. Volume of a cube = a^3, so a = cube root of the volume. a = cube root of 8000 = 20 cm. Check: 20^3 = 20 x 20 x 20 = 8000, which matches 8000.

Let the edge of the cube = a, with volume = 4096 cubic cm. Volume of a cube = a^3, so a = cube root of the volume. a = cube root of 4096 = 16 cm. Check: 16^3 = 16 x 16 x 16 = 4096, which matches 4096.

Let the edge of the cube = a, with volume = 2744 cubic cm. Volume of a cube = a^3, so a = cube root of the volume. a = cube root of 2744 = 14 cm. Check: 14^3 = 14 x 14 x 14 = 2744, which matches 2744.

Let the edge of the cube = a, with volume = 512 cubic cm. Volume of a cube = a^3, so a = cube root of the volume. a = cube root of 512 = 8 cm. Check: 8^3 = 8 x 8 x 8 = 512, which matches 512.

Let the edge of the cube = a, with volume = 3375 cubic cm. Volume of a cube = a^3, so a = cube root of the volume. a = cube root of 3375 = 15 cm. Check: 15^3 = 15 x 15 x 15 = 3375, which matches 3375.

Let the edge of the cube = a = 3 cm. Volume of a cube = a^3, edge multiplied by itself three times. So volume = 3 x 3 x 3. 3 x 3 = 9, and 9 x 3 = 27. So the volume is 27 cubic cm.

Let the edge of the cube = a = 13 cm. Volume of a cube = a^3, edge multiplied by itself three times. So volume = 13 x 13 x 13. 13 x 13 = 169, and 169 x 13 = 2197. So the volume is 2197 cubic cm.

Let the edge of the cube = a = 24 cm. Volume of a cube = a^3, edge multiplied by itself three times. So volume = 24 x 24 x 24. 24 x 24 = 576, and 576 x 24 = 13824. So the volume is 13824 cubic cm.

Let the edge of the cube = a = 12 cm. Volume of a cube = a^3, edge multiplied by itself three times. So volume = 12 x 12 x 12. 12 x 12 = 144, and 144 x 12 = 1728. So the volume is 1728 cubic cm.

Let the edge of the cube = a = 7 cm. Volume of a cube = a^3, edge multiplied by itself three times. So volume = 7 x 7 x 7. 7 x 7 = 49, and 49 x 7 = 343. So the volume is 343 cubic cm.

Let the edge of the cube = a = 10 cm. Volume of a cube = a^3, edge multiplied by itself three times. So volume = 10 x 10 x 10. 10 x 10 = 100, and 100 x 10 = 1000. So the volume is 1000 cubic cm.

Let the edge of the cube = a = 9 cm. Volume of a cube = a^3, edge multiplied by itself three times. So volume = 9 x 9 x 9. 9 x 9 = 81, and 81 x 9 = 729. So the volume is 729 cubic cm.

Let the edge of the cube = a = 22 cm. Volume of a cube = a^3, edge multiplied by itself three times. So volume = 22 x 22 x 22. 22 x 22 = 484, and 484 x 22 = 10648. So the volume is 10648 cubic cm.

Let the edge of the cube = a = 25 cm. Volume of a cube = a^3, edge multiplied by itself three times. So volume = 25 x 25 x 25. 25 x 25 = 625, and 625 x 25 = 15625. So the volume is 15625 cubic cm.

Let the edge of the cube = a = 18 cm. Volume of a cube = a^3, edge multiplied by itself three times. So volume = 18 x 18 x 18. 18 x 18 = 324, and 324 x 18 = 5832. So the volume is 5832 cubic cm.

Let length = l = 18 m, breadth = b = 18 m, height = h = 21 m. The longest pole that fits equals the room’s space diagonal. Diagonal = sqrt(l^2 + b^2 + h^2). l^2 = 324, b^2 = 324, h^2 = 441. Sum = 324 + 324 + 441 = 1089. Diagonal = sqrt(1089) = 33 m. Check: 33^2 = 1089, which matches the sum above.

Let length = l = 2 m, breadth = b = 3 m, height = h = 6 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 = 9, h^2 = 36. Sum = 4 + 9 + 36 = 49. Diagonal = sqrt(49) = 7 m. Check: 7^2 = 49, which matches the sum above.

Let length = l = 4 m, breadth = b = 12 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 = 16, b^2 = 144, h^2 = 324. Sum = 16 + 144 + 324 = 484. Diagonal = sqrt(484) = 22 m. Check: 22^2 = 484, which matches the sum above.

Let length = l = 4 m, breadth = b = 13 m, height = h = 16 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 = 169, h^2 = 256. Sum = 16 + 169 + 256 = 441. Diagonal = sqrt(441) = 21 m. Check: 21^2 = 441, which matches the sum above.

Let length = l = 1 m, breadth = b = 2 m, height = h = 2 m. The longest pole that fits equals the room’s space diagonal. Diagonal = sqrt(l^2 + b^2 + h^2). l^2 = 1, b^2 = 4, h^2 = 4. Sum = 1 + 4 + 4 = 9. Diagonal = sqrt(9) = 3 m. Check: 3^2 = 9, which matches the sum above.

Let length = l = 8 m, breadth = b = 26 m, height = h = 32 m. The longest pole that fits equals the room’s space diagonal. Diagonal = sqrt(l^2 + b^2 + h^2). l^2 = 64, b^2 = 676, h^2 = 1024. Sum = 64 + 676 + 1024 = 1764. Diagonal = sqrt(1764) = 42 m. Check: 42^2 = 1764, which matches the sum above.