Sarah bought a circular marble table top to use as her dining room table. The marble is 4 ft in diameter. Find the cost of the table top at $90 per square yard of marble.
The answer is $452.16 but I'm unsure on how to get there.
Wait, the answer isn't that.
It's $125.60.
That's better
To find the cost of the table top, we need to determine the area of the circular marble top first.
The area of a circle can be calculated using the formula: A = πr^2, where A represents the area and r represents the radius of the circle.
In this case, we are given the diameter, which is 4 ft. The radius (r) is half the diameter, so r = 4 ft / 2 = 2 ft.
Now we can substitute the radius (r) into the formula and calculate the area (A):
A = π(2 ft)^2
A = π * 4 ft^2
A = 4π ft^2
Next, we need to convert the area from square feet to square yards, as the cost is given in dollars per square yard. There are 9 square feet in 1 square yard, so we divide the area (A) by 9:
A = 4π ft^2 / 9
A ≈ 1.41π ft^2
Finally, we can calculate the cost by multiplying the area in square yards (A) by the cost per square yard ($90):
Cost = A * $90
Cost = 1.41π ft^2 * $90
To obtain the exact numerical value, we need to approximate π. We can use the commonly used approximation π ≈ 3.14.
Cost ≈ 1.41 * 3.14 * $90
Cost ≈ $398.22
Therefore, the approximate cost of the table top is $398.22.