The big picture
Two questions came up again and again. What covers the solid? What fills it?
| Idea | Remember | Example |
|---|---|---|
| Skin by net | Six faces, added: 2 × (lb + bh + hl). | 8 × 5 × 3 box: 158 cm² |
| Filling in cubes | l × b × h counts unit cubes. | 8 × 5 × 3 = 120 cm³ |
| Two growth stories | Every edge × k: skin × k², filling × k³. | double the edge: ×4 and ×8 |
| A tin unrolled | The label is 2πr long. Volume is πr²h. | r 7, h 10: 440, 748, 1540 |
| The cone | l = √(r² + h²). Volume is ⅓πr²h. | r 7, h 24: l 25, 704, 1232 |
| Round solids | Sphere: 4πr² and 4/3 πr³. | r 21: 5544 and 38808 |
| The pyramid | Volume ⅓ × base × h. Walls use the slant. | 6 m tent: 48 m³, 60 m² |
| Job picks measure | Covers wants cm². Fills wants cm³. A rope wants cm. | paint, then oil: both |
Open the Class 9 chapter on surface area and volume. Ask both questions as you read.
One habit helps with these solids. Unroll a curved side. Cut a sphere through its centre. Open a solid into its net.