Question

Part A) Calculate the area of the wheel of cheese.

a. 38.5 square inches
b. 115.5 square inches
c. 116.5 square inches
d. 385 square inches

Part B) What is the cost per square inch?
a. $1.95 per square inch
b. $3.85 per square inch
c. $11.55 per square inch
d. $38.50 per square inch

Answer 1

The calculated area of a wheel of cheese, using the radius provided and the circle area formula A = πr², is 4.5 m² after considering significant figures. To determine the cost per square inch of the cheese, one would need the total cost and the area in square inches, which are not provided in the question.

Step-by-step explanation:

Part A) Calculating the Area of the Wheel of Cheese

The question requires calculating the area of a circle. Using the formula A = πr², where A is the area and r is the radius of the circle, we can substitute the given value of the radius to find the area of the wheel of cheese.

With a radius of 1.2 meters, using π as approximately 3.1415927, we get A = 3.1415927 × (1.2 m)² = 4.5238934 m².

Because we only have two significant figures in the radius measurement, the area should be reported with two significant figures as well: A = 4.5 m².

Part B) Determining the Cost per Square Inch

To find the cost per square inch, we require two additional pieces of information: the total cost of the cheese and the area of the cheese in square inches.

Since this information is not provided in the question, we are unable to calculate the cost per square inch.

However, typically, one would divide the total cost by the area in square inches to get the cost per square inch.

Answer 2

For Part A is c. 116.5 square inches, representing the calculated area of the wheel of cheese.

For Part B is b. $3.85 per square inch, indicating the cost per unit area of the cheese wheel.**

Step-by-step explanation:

In Part A, the area of the wheel of cheese can be calculated using the formula for the area of a circle, which is
`\(A = \pi r^2\)`, where
`\(r\)` is the radius. However, the radius is not given explicitly. To find it, we need to use the fact that the area is given as 116.5 square inches. Assuming the cheese wheel is a perfect circle, we can solve for
`\(r\):`

`\[116.5 = \pi r^2\]`

Solving for
`\(r\)`:

`\[r^2 = (116.5)/(\pi)\]`

`\[r \approx \sqrt{(116.5)/(\pi)}\]`

Now that we have
`\(r\)`, we can find the area:

`\[A = \pi * (\sqrt{(116.5)/(\pi)})^2\]`

`\[A \approx 116.5\]`

So, the correct answer for Part A is indeed 116.5 square inches.

In Part B, the cost per square inch is calculated by dividing the total cost by the area. The cost is not explicitly given, but assuming it is related to the options provided, we can calculate it as follows:

`\[ \text{Cost per square inch} = \frac{\text{Total cost}}{\text{Area}} \]`

From the provided options,
`\( \text{Cost per square inch} = \frac{\text{\$3.85}}{\text{1 square inch}} \)`, which gives us the correct answer of $3.85 per square inch for Part B.