1. The volume of a cube is calculated as side³. For a side of 7 m, the volume is 7³ = 343 m³.
2. The volume of a rectangular box is length × breadth × height. For dimensions 16 m, 8 m, and 5 m, the volume is 16 × 8 × 5 = 640 m³.
3. The area of the four walls of a room is 2 × (length + breadth) × height. For dimensions 12 m, 10 m, and 9 m, the area is 2 × (12 + 10) × 9 = 2 × 22 × 9 = 396 m².
4. The volume of a cube is edge³. Given volume is 27a³, so edge³ = 27a³. Taking the cube root, edge = ∛(27a³) = 3a.
5. The surface area of a container with a lid is 2 × (length × breadth + breadth × height + height × length). For dimensions 13 m, 8 m, and 4 m, the area is 2 × (13×8 + 8×4 + 4×13) = 2 × (104 + 32 + 52) = 2 × 188 = 376 m².
6. The volume of a cube is edge³. Given volume is 1331 cm³, so edge³ = 1331. Taking the cube root, edge = ∛1331 = 11 cm.
7. The diagonal of a cube is edge × √3. Given diagonal is 17.32 cm, so edge = 17.32 / √3 ≈ 17.32 / 1.732 = 10 cm. Volume = edge³ = 10³ = 1000 cm³.
8. The total volume of the three cubes is 6³ + 8³ + 10³ = 216 + 512 + 1000 = 1728 cm³. This is the volume of the new cube formed.
9. Joining two cubes of edge 10 m along an edge forms a cuboid of dimensions 20 m × 10 m × 10 m. Surface area = 2 × (20×10 + 10×10 + 10×20) = 2 × (200 + 100 + 200) = 2 × 500 = 1000 m².
10. Volume of a cube is side³. Given volume is 512 cm³, so side³ = 512. Taking the cube root, side = ∛512 = 8 cm.
11. The area of cardboard needed is the total surface area of the box: 2 × (length × breadth + breadth × height + height × length). For dimensions 14 cm, 10 cm, and 5 cm, the area is 2 × (14×10 + 10×5 + 5×14) = 2 × (140 + 50 + 70) = 2 × 260 = 520 cm².
12. The volume of a cylinder is π × radius² × height. For radius 7 cm and height 5 cm, volume = π × 7² × 5 = π × 49 × 5 = 245π cm³.
13. Volume of large sphere = (4/3)π × 2³ = (4/3)π × 8 = 32π/3 cm³. Volume of small sphere = (4/3)π × (2/3)³ = (4/3)π × 8/27 = 32π/81 cm³. Number of small spheres = (32π/3) / (32π/81) = (32π/3) × (81/32π) = 81/3 = 27.
14. For a sphere, volume V = (4/3)πr³ and surface area A = 4πr². Setting V = A numerically: (4/3)πr³ = 4πr². Dividing both sides by 4πr² (assuming r ≠ 0): r/3 = 1, so r = 3.
15. Volume of cylinder = π × radius² × height. Given volume is 392π cm³ and height is 8 cm: π × r² × 8 = 392π. Dividing both sides by π: 8r² = 392. So r² = 392/8 = 49. Therefore, r = √49 = 7 cm.
16. Surface area of a sphere = 4πr². Given area is 448π cm²: 4πr² = 448π. Dividing both sides by 4π: r² = 448/4 = 112. Therefore, r = √112 = √(16×7) = 4√7 cm.
Parent Tip: Review the logic above to help your child master the concept of volume and surface area worksheet pdf.
