Mathematics High School

Stacy is covering the box below with sticky wrapping paper. If the paper cost 2 cents per square centimeter, how much will it cost to cover the entire box.

Stacy Is Covering The Box Below With Sticky Wrapping Paper. If The Paper Cost 2 Cents Per Square Centimeter,

Answers

Answer 1

Given:

The shape of box is a right triangular prism.

Paper cost = 2 cents per square centimeter

To find:

The cost to cover the entire box.

Solution:

In the given right triangular prism, we have 3 rectangle surfaces and 2 triangular surfaces.

Area of a rectangle is

[tex]Area=length\times width[/tex]

Area of rectangle with length 4 cm and width 3 cm is

[tex]A_1=4\times 3=12\text{ cm}^2[/tex]

Area of rectangle with length 4 cm and width 4 cm is

[tex]A_2=4\times 4=16\text{ cm}^2[/tex]

Area of rectangle with length 4 cm and width 5 cm is

[tex]A_3=4\times 5=20\text{ cm}^2[/tex]

Area of a triangle is

[tex]Area=\dfrac{1}{2}\times base\times height[/tex]

Area of triangle with base 3 cm and height 4 cm is

[tex]A_4=\dfrac{1}{2}\times 3\times 4[/tex]

[tex]A_4=\dfrac{12}{2}[/tex]

[tex]A_4=6\text{ cm}^2[/tex]

Bottom and top triangular surfaces are equal.

[tex]A_5=A_4=6\text{ cm}^2[/tex]

Now, total surface area of the box is

[tex]A=A_1+A_2+A_3+A_4+A_5[/tex]

[tex]A=12+16+20+6+6[/tex]

[tex]A=60\text{ cm}^2[/tex]

Paper cost = 2 cents per square centimeter

Cost of 60 square centimeter paper is

[tex]60\times 2=120\text{ cents}[/tex]

Therefore, the cost to cover the entire box is 120 cents or $1.2.

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Answers

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Answers

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