1. **Problem:** Find the nets of the following solids: cube, cuboid, prism, cylinder, cone, and sphere. 2. **Understanding Nets:** A net is a two-dimensional shape that can be folded to form a three-dimensional solid. Each net shows all the faces of the solid laid out flat. 3. **Total Surface Area (TSA):** TSA is the sum of the areas of all the faces of a solid. It tells us how much material is needed to cover the solid. 4. **Formulas for Total Surface Area:** - Cube: $$\text{TSA} = 6a^2$$ where $a$ is the side length. - Cuboid: $$\text{TSA} = 2(lb + bh + hl)$$ where $l$, $b$, and $h$ are length, breadth, and height. - Prism: $$\text{TSA} = \text{Perimeter of base} \times \text{height} + 2 \times \text{Area of base}$$ - Cylinder: $$\text{TSA} = 2\pi r(h + r)$$ where $r$ is radius and $h$ is height. - Cone: $$\text{TSA} = \pi r(l + r)$$ where $l$ is slant height. - Sphere: $$\text{TSA} = 4\pi r^2$$ 5. **Volume of Solids:** Volume measures the space inside a solid. 6. **Volume Formulas:** - Pyramid: $$\text{Volume} = \frac{1}{3} \times \text{Area of base} \times \text{height}$$ - Cube: $$\text{Volume} = a^3$$ - Cuboid: $$\text{Volume} = l \times b \times h$$ - Prism: $$\text{Volume} = \text{Area of base} \times \text{height}$$ - Cylinder: $$\text{Volume} = \pi r^2 h$$ - Cone: $$\text{Volume} = \frac{1}{3} \pi r^2 h$$ - Sphere: $$\text{Volume} = \frac{4}{3} \pi r^3$$ 7. **Summary:** Understanding nets helps visualize solids and their faces. Knowing TSA helps calculate surface coverage. Volume formulas help find the space inside solids. This completes the first question about nets and formulas for surface area and volume.