Question

A cube-shaped hole is cut in a rectangular prism as shown below.

Answer 1

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

Answer 2

Surface area of the prism is 2xy+2xz+2yz 
I think, we can cut hole on the face of the prisma 40x30, and size of the whole will be 5X5X5
hole increases surface area. If side of the cube is "a", then a^2 is the area of the one face of the cube.  
when we are doing the hole, we remove 2 faces and add 4 more faces, so 
 2xy+2xz+2yz-2a^2+4a^2=  2xy+2xz+2yz+2a^2
So, 2*5*40+2*5*30+2*40*30+2*5^2=3150 cm^2
 i hope it helps, it is what i can come up with now