Question

A jewelry store covers small boxes in velvet to wrap items that they sell. The cost of the velvet is $0.02 per square centimeter. Find the surface area of the box shown below to the nearest whole number. Then find the approximate cost of the velvet to cover the box without any overlap to the nearest cent.

Answer 1

The surface area of the box is equal to 214.76 cm².

The approximate cost of the velvet to cover the box is equal to $4.30.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Geometry

Surface Area Formula [Rectangular Prism]:
`\displaystyle \text{SA} = 2(wl + hl + hw)`

• w is width
• l is length
• h is height

Explanation:

Step 1: Define

Identify given.

h = 1.02 cm

l = 8 cm

w = 11 cm

Step 2: Find Surface Area

1. [Surface Area Formula - Rectangular Prism] Substitute in variables:
   
   `\displaystyle \text{SA} = 2 \bigg[ (11 \ \text{cm})(8 \ \text{cm}) + (1.02 \ \text{cm})(8 \ \text{cm}) + (1.02 \ \text{cm})(11 \ \text{cm}) \bigg]`
2. Evaluate [Order of Operations]:
   
   `\displaystyle \text{SA} = \boxed{ 214.76 \ \text{cm}^2}`

∴ the surface area of the small box is equal to 214.76 cm².

Step 3: Find Cost

To find the cost of covering the entire box, we can simply multiply the unit cost to the surface area to find out the net price:

`\displaystyle\begin{aligned}\text{Cost} & = \frac{\$ 0.02}{\text{cm}^2} \bigg( 214.76 \ \text{cm}^2 \bigg) \\& = \$ 4.2952 \\& \approx \boxed{ \$ 4.30 }\end{aligned}`

∴ the cost to cover the entire surface of the box is equal to approximately $4.30.

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Topic: Geometry