The problem is asking for the length of arc VW in circle UU, given that ∠VUW = 20 degrees and the area of the shaded sector is 25/18 π.

Step 1: Determine the ratio of ∠VUW to a full circle.
A full circle is 360 degrees. The ratio of ∠VUW to a full circle is therefore 20/360 = 1/18.

Step 2: Determine the area of the full circle.
The area of the shaded sector is 25/18 π, which is 1/18 of the area of the full circle. Therefore, the area of the full circle is (25/18 π) * 18 = 25π.

Step 3: Determine the radius of the circle.
The area of a circle is given by the formula A = πr², where r is the radius of the circle. Solving for r gives r = sqrt(A/π) = sqrt(25π/π) = sqrt(25) = 5.

Step 4: Determine the circumference of the circle.
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Substituting r = 5 gives C = 2π * 5 = 10π.

Step 5: Determine the length of arc VW.
The length of arc VW is 1/18 of the circumference of the circle. Therefore, the length of arc VW is (1/18) * 10π = 10/18 π = 5/9 π.

Question

The problem is asking for the length of arc VW in circle UU, given that ∠VUW = 20 degrees and the area of the shaded sector is 25/18 π.

Step 1: Determine the ratio of ∠VUW to a full circle.
A full circle is 360 degrees. The ratio of ∠VUW to a full circle is therefore 20/360 = 1/18.

Step 2: Determine the area of the full circle.
The area of the shaded sector is 25/18 π, which is 1/18 of the area of the full circle. Therefore, the area of the full circle is (25/18 π) * 18 = 25π.

Step 3: Determine the radius of the circle.
The area of a circle is given by the formula A = πr², where r is the radius of the circle. Solving for r gives r = sqrt(A/π) = sqrt(25π/π) = sqrt(25) = 5.

Step 4: Determine the circumference of the circle.
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Substituting r = 5 gives C = 2π * 5 = 10π.

Step 5: Determine the length of arc VW.
The length of arc VW is 1/18 of the circumference of the circle. Therefore, the length of arc VW is (1/18) * 10π = 10/18 π = 5/9 π.

Knowee AI · Accepted Answer

The problem is asking for the length of arc VW in circle UU, given that ∠VUW = 20 degrees and the area of the shaded sector is 25/18 π.

Step 1: Determine the ratio of ∠VUW to a full circle.
A full circle is 360 degrees. The ratio of ∠VUW to a full circle is therefore 20/360 = 1/18.

Step 2: Determine the area of the full circle.
The area of the shaded sector is 25/18 π, which is 1/18 of the area of the full circle. Therefore, the area of the full circle is (25/18 π) * 18 = 25π.

Step 3: Determine the radius of the circle.
The area of a circle is given by the formula A = πr², where r is the radius of the circle. Solving for r gives r = sqrt(A/π) = sqrt(25π/π) = sqrt(25) = 5.

Step 4: Determine the circumference of the circle.
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Substituting r = 5 gives C = 2π * 5 = 10π.

Step 5: Determine the length of arc VW.
The length of arc VW is 1/18 of the circumference of the circle. Therefore, the length of arc VW is (1/18) * 10π = 10/18 π = 5/9 π.

In circle UU, mangle, V, U, W, equals, 20, degrees∠VUW=20 ∘ and the area of shaded sector = start fraction, 25, divided by, 18, end fraction, pi 1825 π. Find the length of arc, V, W VW⌢ . Express your answer as a fraction times piπ.

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In circle UU, mangle, V, U, W, equals, 20, degrees∠VUW=20 ∘ and the area of shaded sector = start fraction, 25, divided by, 18, end fraction, pi 1825​ π. Find the length of arc, V, W VW⌢ . Express your answer as a fraction times piπ.

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In circle UU, mangle, V, U, W, equals, 20, degrees∠VUW=20 ∘ and the area of shaded sector = start fraction, 25, divided by, 18, end fraction, pi 1825 π. Find the length of arc, V, W VW⌢ . Express your answer as a fraction times piπ.