3.5 Surface Area of Prisms and Cylinders

The total surface area (SA) of a rectangular prism is given by the formula: SA = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.

The lateral surface area (LSA) of a rectangular prism is given by the formula: LSA = 2h(l + w), where h is the height, l is the length, and w is the width.

The total surface area (SA) of a cylinder is given by the formula: SA = 2 ext{π}r^2 + 2 ext{π}rh, where r is the radius and h is the height.

The lateral surface area (LSA) of a cylinder is given by the formula: LSA = 2 ext{π}rh, where r is the radius and h is the height.

The total surface area is 2(5*3 + 5*4 + 3*4) = 2(15 + 20 + 12) = 2(47) = 94 cm².

The lateral surface area is LSA = 2h(l + w) = 2*9(7 + 3) = 2*9*10 = 180 cm².

Using the formula SA = 2 ext{π}r^2 + 2 ext{π}rh, we find SA = 2*3.14*4^2 + 2*3.14*4*10 = 100.48 + 251.2 = 351.68 cm².

Using the formula LSA = 2 ext{π}rh, we find LSA = 2*3.14*5*12 = 376.8 cm².

Surface area is the total area that the surface of a three-dimensional object occupies.

Total surface area includes all surfaces of the 3D shape, while lateral surface area only includes the sides, excluding the top and bottom.