Answer:
The surface area of the composite figure = 1172.08 inches²
Explanation:
* Lets explain the figure
- There is a cylinder with diameter 8 inches and height 9 inches
- Rectangular prism with dimensions 16 , 11 , 11 inches
- The surface area of the cylinder will be the curved area and the
top base
- The surface area of the prism will be the surface area of one base ,
four side faces and top face which is the remaining from the subtraction
of the rectangular base and the circular base
* Lets solve the problem
# The surface area of the cylinder
∵ The diameter of the base of the cylinder is 8 inches
∵ The diameter = twice the radius
∴ 8 = 2r ⇒ divide both sides by 2
∴ r = 4 inches
∵ The area of the circle = πr²
∴ The area of the base = π(4)² = 16π inches²
∵ π = 3.14
∴ The area of the base = 16(3.14) = 50.24 inches²
∵ The area of the curved surface = 2πrh
∵ r = 4 inches and h = 9 inches
∴ The area of the curved surface = 2(3.14)(4)(9) = 226.08 inches²
∴ The surface area of the cylinder = 226.08 + 50.24 = 276.32 inches²
# The surface area of the rectangular prism
∵ The dimensions of its base are 16 and 11 inches
∵ The area of the rectangle = length × width
∴ The area of the lower base = 16 × 11 = 176 inches²
∵ The area of the top face = area of the rectangle - area of the circle
∵ The area of the rectangle = 176 inches²
∵ The area of the circle = 50.24
∴ The area of the top face = 176 - 50.24 = 125.76 inches²
- There are two side faces with dimensions 16 and 11 inches
∴ The area of the two faces = 2 × 16 × 11 = 352 inches²
- There are two faces with dimensions 11 and 11 inches
∴ The area of the two faces = 2 × 11 × 11 = 242 inches²
∵ The surface area of the rectangular prism is the sum of the 6 faces
∴ The surface area of the prism = 176 + 125.76 + 352 + 242
∴ The surface area of the prism = 895.76 inches²
- The surface area of the composite figure is the sum of the surface
area of the cylinder and the surface area of the prism
∵ The surface area of the cylinder = 276.32 inches²
∵ The surface area of the prism = 895.76 inches²
∴ The surface area of the composite figure = 276.32 + 895.76
∴ The surface area of the composite figure = 1172.08 inches²