Question

You need to polish your circular dining room table, which has a diameter of 7 feet. The label on the polish can claims coverage for 100 square feet, but you notice that the can is only about one-half full. Will you have enough polish to finish your table? Explain.

Short answer

Answer: Yes, there will be enough polish to finish the table.

Step-by-step solution

Find the diameter of the table

We are given the diameter of the circular table: 7 feet.

Calculate the radius

To find the area of the table, we first need to compute the radius. The radius is half of the diameter: \(radius=\frac{diameter}{2}\). The diameter of the table is 7 feet, so the radius is \(\frac{7}{2}=3.5\) feet.

Calculate the area of the table

Now we can compute the area of the table using the formula for the area of a circle: \(Area=\pi r^2\). With a radius of 3.5 feet, the area of the table is: \(Area=\pi (3.5)^2\approx 38.48\) square feet.

Calculate remaining polish coverage

The polish can claims coverage for 100 square feet. However, the can is only about one-half full, meaning we only have 50% of the polish available for use. Therefore, the remaining coverage from the polish is: 0.5 * 100 = 50 square feet.

Compare the table's area to the remaining polish coverage

The table's area is approximately 38.48 square feet, while the remaining polish coverage is 50 square feet. Since the table's area is smaller than the available polish coverage, there is enough polish to finish the table. So, yes, there will be enough polish to finish the table.