Explore Chapter 12: Mastering Combined Solids with structured data tables for quick revision. Understand surface areas and volumes of combined solids, conversion of solids, geometric applications, real-life problem-solving, and key formulas in an organized format, helping CBSE students grasp concepts clearly and retain them easily.
| Object Name | Basic Solid Components | Key Dimensions | Surface Area Formula (Inferred) | Volume Formula (Inferred) | Calculated Value | Units |
|---|---|---|---|---|---|---|
| Playing Top (Lattu) | Cone and Hemisphere | Total Height: $5$ cm; Diameter: $3.5$ rcm; Cone Height: $3.25$ cm; Slant Height ( $l$ ): $3.7$ cm | $2\pi r^{2} + \pi rl$ | $\frac{2}{3}\pi r^{3} + \frac{1}{3}\pi r^{2}h$ | $39.6$ | cm $^{2}$ |
| Decorative Block | Cube and Hemisphere | Cube Edge ( $a$ ): $5$ cm; Hemisphere Diameter: $4.2$ cm | $6a^{2} - \pi r^{2} + 2\pi r^{2}$ | $a^{3} + \frac{2}{3}\pi r^{3}$ | $163.86$ | cm $^{2}$ |
| Wooden Toy Rocket | Cone and Cylinder | Total Height: $26$ cm; Cone Height ( $h$ ): $6$ cm; Cone Diameter: $5$ cm; Cylinder Diameter: $3$ cm; Cylinder Height ( $h'$ ): $20$ cm | $(\text{CSA}{\text{cone}} + \text{Base}{\text{cone}} - \text{Base}{\text{cyl}}) + (\text{CSA}{\text{cyl}} + \text{Base}_{\text{cyl}})$ | $\frac{1}{3}\pi r^{2}h + \pi r'^{2}h'$ | $63.585$ (Orange); $195.465$ (Yellow) | cm $^{2}$ |
| Bird-bath | Cylinder and Hemisphere | Cylinder Height ( $h$ ): $1.45$ m; Radius ( $r$ ): $30$ cm | $2\pi rh + 2\pi r^{2}$ | $\pi r^{2}h - \frac{2}{3}\pi r^{3}$ | $3.3$ | m $^{2}$ |
| Industrial Shed | Cuboid and Half Cylinder | Cuboid: $15$ m $\times$ $7$ m $\times$ $8$ m; Cylinder Diameter: $7$ m; Cylinder Height: $15$ m | Not in source | $lbh + \frac{1}{2}\pi r^{2}h$ | $1128.75$ | m $^{3}$ |
| Juice Glass | Cylinder and Hemisphere | Inner Diameter: $5$ cm; Height: $10$ cm | Not in source | $\pi r^{2}h - \frac{2}{3}\pi r^{3}$ | $163.54$ | cm $^{3}$ |
| Solid Toy | Hemisphere and Cone | Cone Height ( $h$ ): $2$ cm; Base Diameter: $4$ cm | Not in source | $\frac{2}{3}\pi r^{3} + \frac{1}{3}\pi r^{2}h$ | $25.12$ | cm $^{3}$ |
| Gulab Jamun | Cylinder and two Hemispheres | Total Length: $5$ cm; Diameter: $2.8$ cm | $2\pi rh + 2(2\pi r^{2})$ | $\pi r^{2}h + 2(\frac{2}{3}\pi r^{3})$ | Not in source | cm $^{3}$ |
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