proof from Archimedes for the area of the circle formula

The sector of a circle has an area of 231.3 sq in. and a central angle of 6515'. What is the radius of the circle? Round the answer to 1 decimal place.

A lawn roller in the shape of a right circular cylinder has a radius of length 18 in. and a length height of 4 ft. Find the area rolled during one complete revolution of the roller. Use the calculator value of , and give the answer to the nearest square foot.

Laying Phone Cable City A lies on the north bank of a river that is 1 mile wide. You need to run a phone cable from City A to City B, which lies on the opposite bank 5 miles down the river. You will lay L miles of the cable along the north shore of the river, and from the end of that stretch of cable you will lay W miles of cable running under water directly toward City B. See Figure 2.108. Figure 2.108 You will need the following fact about right triangles: A right triangle has two legs, which meet at the right angle, and the hypotenuse, which is the longest side. An ancient and beautiful formula, the Pythagorean theorem, relates the lengths of the three sides: Lengthofhypotenuse=Lengthofoneleg2+Lengthofotherleg2 a. Find an appropriate right triangle that shows that W=1+(5L)2 b. Find a formula for the length of the total phone cable P from City A to City B as a function of L. c. Make a graph of the total phone cable length P as a function of L, and explain what the graph is showing. d. What value of L gives the least length for the total phone cable? Draw a picture showing the least-length total phone cable.

Radius of the Moon As viewed from the earth, the angle subtended by the full moon is 0.518. Use this information and the fact that the distance AB from the earth to the moon is 236,900 mi to find the radius of the moon.

Use the Pythagorean Theorem to find the length of the leg in the triangle shown below.

A landscaper wants to put a square reflecting pool next to a triangular deck, as shown below. The triangular deck is a right triangle, with legs of length 9 feet and 11 feet, and the pool will be adjacent to the hypotenuse. (a) Use the Pythagorean Theorem to find the length of a side of the pool. Round your answer to the nearest tenth of a foot. (b) Find the exact area of the pool.

A circle can be inscribed in the trapezoid shown. Find the area of that circle.

Find radius r. All dimensions are in millimeters.

Find the area of an equilateral triangle with apothem a = 4.6 in. and perimeter P=27.63 in.