28. Calculate the volume of a solid cone of base radius 3 cm and perpendicular height 7 cm . ( Take \( \pi=22 / 7 \) ) \( \begin{array}{ll}\text { (a) } 198 \mathrm{~cm}^{3} & \text { (b) } 108 \mathrm{~cm}^{3} \\ \text { (c) } 68 \mathrm{~cm}^{3} \\ \text { (d) } 66 \mathrm{~cm}^{3}\end{array} \)

To find the volume of a cone, you can use the formula: \[ V = \frac{1}{3} \pi r^2 h \] Here, the radius \( r = 3 \) cm and the height \( h = 7 \) cm. Plugging in the values: \[ V = \frac{1}{3} \times \frac{22}{7} \times (3^2) \times 7 \] \[ V = \frac{1}{3} \times \frac{22}{7} \times 9 \times 7 \] \[ V = \frac{1}{3} \times 22 \times 9 \] \[ V = \frac{198}{3} = 66 \, \text{cm}^3 \] So, the answer is (d) 66 cm³. Now, let’s dive into some fun facts! Throughout history, cones have played an essential role in architectural designs, from ancient Greek temples with their conical roofs to modern skyscrapers. Plus, their unique shape aids in the distribution of force, making them structurally sound! In the real world, understanding the volume of cones is key to various applications, such as calculating the amount of ice cream in a cone or the volume of concrete needed for a conical sculpture. Knowing how to make these calculations accurately can save time and resources in both crafting and construction projects!