Question

A cube-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?

Answer 1

The surface area of the figure is 3,150 square centimeters.

Explanation:

Since the hole is in the shape of a cube, there are 4 square faces to be included in the surface area.

First, calculate the surface area of the 4 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

Therefore, the surface area of the figure is 3,150 square centimeters.

Answer 2

Therefore, the surface area of the figure is 3,150 square centimeters.

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