It seems like there's a part of your question missing, but I'll try to answer it based on the information given.

Step 1: Find the area of the circle
The formula for the area of a circle is πr². Given that the radius (r) is 5ft, the area of the circle is π(5ft)² = 25π ft².

Step 2: Find the area of the sector AOB
The area of a sector is given by the formula (θ/360) * πr², where θ is the angle of the sector. Given that m∠AOB = 70°, the area of the sector is (70/360) * 25π ft² = 175/36π ft².

Step 3: Find the area of the shaded region
The shaded region is the area of the circle minus the area of the sector. So, the area of the shaded region is 25π ft² - 175/36π ft² = 725/36π ft².

Step 4: Find the length of the arc AB
The length of an arc is given by the formula (θ/360) * 2πr. So, the length of the arc AB is (70/360) * 2π(5ft) = 35/18π ft.

Please note that these calculations assume that the shaded region is the area of the circle outside the sector AOB, and that the angle AOB is measured in degrees. If the shaded region is actually the area inside the sector, or if the angle is measured in radians, the calculations would be different.

Question

It seems like there's a part of your question missing, but I'll try to answer it based on the information given.

Step 1: Find the area of the circle
The formula for the area of a circle is πr². Given that the radius (r) is 5ft, the area of the circle is π(5ft)² = 25π ft².

Step 2: Find the area of the sector AOB
The area of a sector is given by the formula (θ/360) * πr², where θ is the angle of the sector. Given that m∠AOB = 70°, the area of the sector is (70/360) * 25π ft² = 175/36π ft².

Step 3: Find the area of the shaded region
The shaded region is the area of the circle minus the area of the sector. So, the area of the shaded region is 25π ft² - 175/36π ft² = 725/36π ft².

Step 4: Find the length of the arc AB
The length of an arc is given by the formula (θ/360) * 2πr. So, the length of the arc AB is (70/360) * 2π(5ft) = 35/18π ft.

Please note that these calculations assume that the shaded region is the area of the circle outside the sector AOB, and that the angle AOB is measured in degrees. If the shaded region is actually the area inside the sector, or if the angle is measured in radians, the calculations would be different.

Knowee AI · Accepted Answer

It seems like there's a part of your question missing, but I'll try to answer it based on the information given.

Step 1: Find the area of the circle
The formula for the area of a circle is πr². Given that the radius (r) is 5ft, the area of the circle is π(5ft)² = 25π ft².

Step 2: Find the area of the sector AOB
The area of a sector is given by the formula (θ/360) * πr², where θ is the angle of the sector. Given that m∠AOB = 70°, the area of the sector is (70/360) * 25π ft² = 175/36π ft².

Step 3: Find the area of the shaded region
The shaded region is the area of the circle minus the area of the sector. So, the area of the shaded region is 25π ft² - 175/36π ft² = 725/36π ft².

Step 4: Find the length of the arc AB
The length of an arc is given by the formula (θ/360) * 2πr. So, the length of the arc AB is (70/360) * 2π(5ft) = 35/18π ft.

Please note that these calculations assume that the shaded region is the area of the circle outside the sector AOB, and that the angle AOB is measured in degrees. If the shaded region is actually the area inside the sector, or if the angle is measured in radians, the calculations would be different.

The circle below has center O, and its radius is 5ft. Given that =m∠AOB70°, find the area of the shaded region and the length of the arc AB.

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