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1 ccelerated G Trigonometry ircle pplications Name & ate ircles: SETOR θ R irections: onsider to answer the following questions. 1) Find the circumference of the circle. Exact: pproximate: 2) Find the area of the circle. Exact: pproximate: 3) Find the length of. 4) Find the area of the sector bound by,, and. 5) Find the length of. 6) Find the area of the sector bound by,, and. 7) If the length of E is 40cm, what is me?
2 8) onsider the circle below with center O (circle O). ) Find the circumference of O. O 70 5 inches ) Find the length of. ) Find the area of O. ) Find the area of the sector bound by points O. E) Find the area of O. F) Find the area of the shaded region. 9) Find the area of the shaded region in L below. L P
3 10) Find the area of the shaded region in 11) Suppose a baseball field is shaped like a 12) If the length of H 2.75 and O=3.5, quarter-circle with a radius of 350 feet. What find m O. is the area of the outfield (shaded region)? 13) Find the area of the shaded region. 14) Find the area of the shaded region.
4 15) with a diameter of 12cm is packed in a square case which measures 13cm along a side. How much space is around the? 16) rectangular pool is 24 feet wide and 30 feet long. It is surrounded by a walk that is 2 feet wide, as shown below. ) What is the outer perimeter of the walkway? ) What is the area of the walkway? 17) RSTU is a square with a side length of 18 units. semicircle is placed so its diameter lies along one side of the square and is equal in length to the side of the square. To the nearest tenth of a unit, what is the area of the shaded region? 18) The sketch below shows three circular disks cut from a rectangular sheet of metal. Explain how you can tell the sketch is labeled incorrectly. How do you think the sketch should be labeled? Using your labels, calculate the amount of metal that is wasted.
5 ccelerated G ircle pplications Name & ate 19) Mr. Pachapur has a cow tied by a 25 meter rope to the corner of the barn shown. fence prevents the cow from entering the garden. The figure is not drawn to scale. Find the exact area of the grazing area of the cow without a calculator.
6 20) Find the exact area of the shaded region if is a square with side lengths of 3. & are centers of the circles and & lie on points of intersection. 21) QR is the arc of a circle with center P. If the length of arc QR is 6, what is the area of sector PQR? Leave your answer in terms of pi. Q P 30 R 22) In the figure below, the circle with center O is inscribed in a square. What is the area of the shaded portion of the circle in terms of pi? 2 O
7 ccelerated G ircle pplications Name & ate 23) Humpty umpty bought a 100 foot hose to water his grass and garden around his house. diagram of Humpty s house is below. Sketch and label the region where the hose can reach. Find the area of the region. 100 feet 30 feet 60 feet 50 feet 24) In the figure below, a circle with radius 1 is inscribed in an equilateral triangle. What is the exact area of the triangle? What is the approximate area of the space between the triangle and the circle?
8 25) The figure below consists of two circles that have the same center. If the unshaded area is 64 square inches and the smaller circle has a radius of 6 inches, what is the radius, in inches, of the larger circle? 26) In the figure below, XYZ is equilateral, with side length 2. If WY is a diameter of the circle, with \ center O, find the area of the circle. Y O X W Z 27) In the figure below, E and are each perpendicular to E. If x = y, the length of is 4, and the length of is 8, what is the length of E? y x E
9 ccelerated G ircle pplications Name & ate 28) The length of the diagonal of a square is j + 3. Find the area of the square in terms of j. 29) In the figure below, the two circles have the same center, and the unshaded region has an area twice that of the inner circle. ) If the area of the smaller circle is 4, what is the ratio of the radius of the inner circle to that of the outer circle? ) If the area of the smaller circle is 10, what is the ratio of the radius of the inner circle to that of the outer circle? 30) If the perimeter of square WXYZ is 16 2, what is the area of square EFGH? F X 45 G W Y E Z H
10 31) In the figure below, the length of arc is 1 9 the circumference of a circle with center. If has length 6, what is the area of the sector of the circle show below? 32) In the figure below, E is equilateral. If =, = E, and FG is a rectangle, what fraction of the area of E is shaded? G F E 33) The figure below is composed of two semicircles and one triangle. What is the exact perimeter of the figure? 10 6
11 34) The figure below is a regular polygon with a side length of 18 in, inscribed in a circle. Find the area of the shaded region. irections: Each diagram contains a regular polygon and a circle. Find the exact area of the unshaded region. 35) 8 36) 6
12 37) In rectangle, = 2 and points E and F lie on so that E and F trisect as shown. ) If = 3, what is the exact ratio of the area of EF to the area of rectangle? E F ) If = 6, what is the exact ratio of the area of EF to the area of rectangle? E F
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