Class 10 Chapter 12, Surface Areas and Volumes, focuses on calculating the surface area and volume of various solids. Key formulas include the surface area and volume of shapes like cubes, spheres, cylinders, and cones.
The surface area of a cube is given by $6a^2$ (where a is the side length), and the volume is $a^3$.
The surface area of a sphere is $4\pi r^{2}$, and its volume is $\frac{4}{3}\pi r^{3}$, where r is the radius.
For a cylinder, the surface area is $2πr(r+h)$, and the volume is $πr^2h$, where r is the radius and h is the height.
The volume of a cone is $\frac{1}{3}\pi r^{2}h$, and the volume of a frustum of a cone is $\frac{1}{3}\pi h({r_1}^2 +r_1 r_2 +{r_2}^2)$, where $r_1$ and $r_2$ are the radii of the two circular ends, and h is the height.