Question

Two cardboard boxes are stacked on top of each other. 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. Find the surface area of the composite shape. Select the correct answer.

A. 1,605 in²
B. 1,506 in²
C. 1,560 in²

Answer 1

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.

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,

`Surface area cube, A _(Cube) = 5a^(2)`

( Only 5 sides area considered )

Where, a - Side of cube

From given, a = 10 inches

From the surface area equation,

`A_(Cube) = 5 (10)^(2)`

= (5)(100)

= 500

Surface area of cube = 500 square inches

Step:3

Formula surface area of rectangular prism,

`A _(rectangular prism) = 2 (wl+lh+hw)-100`

Where, w - Width

l - Length

h - Height

From the given values.

w = 15 inches

l = 20 inches

h = 8 inches

Surface area equation becomes,

`A _(rectangular prism) = 2 ((20)(15)+(20)(8)+(8)(15))-100`

= 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.

Answer 2

The surface area of the composite shape is 1560 square inches

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