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

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841

13.46

step-by-step explanation:

16.80 x .20 = 13.46