## Summary

Curved surface area (CSA) is the area of the curved surfaces for the solid. The remaining surfaces of the solid are the flat or the non-curved surfaces.

In a cone, the flat surface is the circular area of the base. In a cylinder, the flat surfaces are the top and bottom circular areas. A sphere has no flat surface, whereas a cuboid and a cube have only flat surfaces.

The flat surface area and the CSA of a solid together add up to the total surface area (TSA) for the solid.

Total Surface Area (TSA) = Curved Surface Area (CSA) + Areas of Flat Surfaces.

Diagonal of a cuboid = $\sqrt{{\text{l}}^{\text{2}}\text{+}{\text{b}}^{\text{2}}\text{+}{\text{h}}^{\text{2}}}$ where l = length, b = breadth, h = height.

Diagonal of a cube = √3×a where a is side of a cube.

Area of a four walls of a room = 2(l + b)h where l = length, b = breadth, h = height.

**Hollow cylinder**

Let R and r be the external an internal radii of a hollow cylinder, and h be the height.

1) Thickness of Cylinder = R - r

2) Area of a cross section = π(R^{2} - r^{2})

3) External curved surface area = 2πRh

4) Internal curved surface area = 2πrh

5) Total surface area of a cylinder (TSA) = External curved surface area + Internal curved surface area + Area of two ends.

= 2πRh + 2πrh + 2π(R^{2} - r^{2}) = 2π( Rh + rh + R^{2} - r^{2 })

6) Volume of the material = πR^{2}h - πr^{2}h = π(R^{2} - r^{2})h.