Acube-shaped hole is cut in a rectangular prism as shown below. if x = 5 cm, y = 40 cm, and z = 30 cm, what is the surface area of the figure?

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

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step-by-step explanation: