Question

A spherical tank with radius 35 ft is partially filled with oil. The angle between two radii of the sphere that have endpoints on diametrically opposite points on the circle of the oil surface is 125°. Find the area of the oil surface. Round your answer to the nearest ft².​

Answer 1

3028 ft²

Explanation:

You want the area of a circle in a sphere of radius 35 ft when it subtends a central angle of 125°.

Radius

Angle KOB in the diagram will be half the measure of angle AOB, so is ...

∠KOB = 1/2(∠AOB) = 1/2(125°) = 62.5°

The measure of the radius KB is ...

sin(62.5°) = KB/OB

KB = OB·sin(62.5°) = (35 ft)·sin(62.5°) ≈ 31.0454 ft

Area

The area of the circle is given by ...

A = πr²

A = π(31.0454 ft)² ≈ 3028 ft²

The area of the circular surface of the oil is about 3028 ft².

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