Chapter 12.2, Problem 41HP

To determine

To compare the surface area of prism and cylinder.

Explanation of Solution

Formula used:

Total surface area of any solid = Lateral surface area + 2(Base area)

A prism is solid that are polygons and sides are flat surfaces. There is rectangular prism, hexagonal prism and many more.

Technically a cylinder is not a prism, however it is extremely similar. If we imagine a prism with regular polygons for bases, and we increase the number of sides, the solid will look more like a cylinder. Therefore a cylinder can be considered as a prism with an infinite number of faces.

• Total surface area of square prism:

Lateral surface area = perimeter $\times$ height of prism = $4ah$

Total surface area = $4ah+2a^2$

• Total surface area of cylinder

Lateral surface area = perimeter $\times$ height of cylinder = $2\pi rh$

Total surface area = $2\pi rh+2\pi r^2$

By comparing the above two formulas we can conclude that surface area of prism and cylinder are almost same.