Answer:
Therefore, the surface area of the figure is 3,150 square centimeters.
Step-by-step explanation:
Since the hole is in the shape of a cube, there are four square faces to be included in the surface area.
First, calculate the surface area of the four square faces of the hole.
SAhole = 4(5 cm)(5 cm)
= 4(25 sq cm)
= 100 sq cm
Next, calculate the surface area of the rectangular prism (ignoring the hole, for now).
SArect = 2(front face) + 2(side face) + 2(top face)
= 2(40 cm)(5 cm) + 2(30 cm)(5 cm) + 2(40 cm)(30 cm)
= 400 sq cm + 300 sq cm + 2,400 sq cm
= 3,100 sq cm
Since the top and bottom rectangles of the prism have a hole in them, subtract these parts from the surface area of the prism.
SAparts = 2(area of top of hole)
= 2(5 cm)(5 cm)
= 50 sq cm
Finally, calculate the total surface area of the figure.
SAtotal = hole + rectangular prism - parts
= 100 sq cm + 3,100 sq cm - 50 sq cm
= 3,150 sq cm