The surface area of the composite shape is 1560 square inches
Step-by-step explanation:
The surface area of the top cardboard is,
SA = 5 x area of each side
Because one side is attached with another cardboard box . So while finding the area only 5 sides are calculated.
SA = 5 ( 10 x 10)
= 500 square inches
The surface area of the rectangular prism cardboard,
Given that,
l = 20 in
w =15 in
h = 8 in
A = 2(lw + wh + hl) - 100
We are subtracting 100 because it is the area of one side of the square cardboard box on top of the rectangular prism box .
A = 2(300 + 120 + 160) - 100
= 2(580) - 100
= 1160-100
= 1060 square inches
Total surface area = SA + A
= 500 + 1060
= 1560 square inches
The surface area of composite shape is 1760 square inches, if two cardboard boxes are stacked on top of each other. The top box is a cube with sides of 10 in and the bottom box is a rectangular prism with a length of 20 in, width of 15 in, and height of 8 in.
Step-by-step explanation:
The given is,
The top box is a cube with sides of 10 in
The bottom box is a rectangular prism with a length of 20 in, width of 15 in, and height of 8 in.
Step:1
Surface area of composite figure = Surface area of cube +
Surface area of rectangular prism
Step:2
Formula for surface area of cube,
[tex]Surface area cube, A _{Cube} = 5a^{2}[/tex]
( Only 5 sides area considered )
Where, a - Side of cube
From given, a = 10 inches
From the surface area equation,
[tex]A_{Cube} = 5 (10)^{2}[/tex]
= (5)(100)
= 500
Surface area of cube = 500 square inches
Step:3
Formula surface area of rectangular prism,
[tex]A _{rectangular prism} = 2 (wl+lh+hw)-100[/tex]
Where, w - Width
l - Length
h - Height
From the given values.
w = 15 inches
l = 20 inches
h = 8 inches
Surface area equation becomes,
[tex]A _{rectangular prism} = 2 ((20)(15)+(20)(8)+(8)(15))-100[/tex]
= 2 ( 300 + 160 + 120 )-100
= 2 (580)-100
Surface area of rectangular prism = 1060 square inches
From the step 1,
Surface area of composite shape = 500+1060
= 1560 square inches
Result:
The surface area of composite shape is 1560 square inches.
