Answer: Rounding this to two decimal places, the cost of the glass used is approximately $36.25.
Assumptions made:
1. The glass used is made of a single piece and not multiple pieces joined together.
2. The cost of one piece of glass remains constant, regardless of the size or shape of the glass.
3. No wastage or breakage of glass occurred during the construction of the jewelry box.
Step-by-step explanation:) To calculate the amount of glass Tracy used for the jewelry box, we need to find the surface area of the box. The surface area of a rectangular prism (like the jewelry box) can be found using the formula:
Surface Area = 2lw + 2lh + 2wh
where l is the length, w is the width, and h is the height of the box.
Using the given measurements of the jewelry box (20 cm by 12 cm by 8 cm), we can substitute these values into the formula:
Surface Area = 2(20 cm)(12 cm) + 2(20 cm)(8 cm) + 2(12 cm)(8 cm)
Simplifying this equation, we get:
Surface Area = 480 cm² + 320 cm² + 192 cm²
Surface Area = 992 cm²
So Tracy used approximately 992 cm² of glass for the jewelry box.
b) To calculate the cost of the glass, we need to know the total area of the glass used. From part (a), we know that Tracy used 992 cm² of glass.
Given that one piece of glass has an area of 100 cm² and costs $3.65, we can calculate the cost of the glass used by dividing the total area of the glass by the area of one piece of glass and then multiplying it by the cost of one piece.
Cost of the glass = (Total area of glass / Area of one piece of glass) * Cost of one piece
Substituting the values into the formula:
Cost of the glass = (992 cm² / 100 cm²) * $3.65
Simplifying this equation, we get:
Cost of the glass = 9.92 * $3.65
Cost of the glass = $36.248
Rounding this to two decimal places, the cost of the glass used is approximately $36.25.
Assumptions made:
1. The glass used is made of a single piece and not multiple pieces joined together.
2. The cost of one piece of glass remains constant, regardless of the size or shape of the glass.
3. No wastage or breakage of glass occurred during the construction of the jewelry box.