A rectangular piece of cloth is 3 ft. by 6 ft. What is the area of the largest circle
that can be cut from the cloth? Round to nearest square inch.
To find the area of the largest circle that can be cut from the cloth, we need to determine the maximum diameter of the circle that can fit within the given rectangular piece of cloth.
Let's start by finding the longer side of the rectangle, which is 6 ft. Since the diameter of the circle cannot exceed this measurement, the maximum diameter we can have is 6 ft.
To calculate the area of a circle, we need to know the radius. The radius is half the diameter, so in this case, the radius would be 6 ft / 2 = 3 ft.
The formula for calculating the area of a circle is A = πr², where A is the area and r is the radius. So, the area of the circle would be A = π(3 ft)².
To round the answer to the nearest square inch, we need to convert the area from square feet to square inches. Since 1 square foot is equal to 144 square inches, the area of the circle would be:
A = π(3 ft)² = π(9 ft²) = 9π ft²
A ≈ 9π × 144 in² (since 1 ft² = 144 in²)
A ≈ 1296π in²
Finally, we can round the result to the nearest square inch:
A ≈ 1296π in² ≈ 1296 × 3.14 in² ≈ 4069.44 in²
Rounding to the nearest square inch, the area of the largest circle that can be cut from the cloth is approximately 4069 in².
The largest diameter is 3 ft.
A = pi * r*2