Date: 7 October 2006, Source Edited version of Image:Pi-unrolled.gif., Author John Reid
1) Find the circumference of a circle given the length of a radius. Leave your answer two ways: in terms of \(\pi\) and rounded to the nearest tenth.
a) radius = \(8\) in.
b) radius = \(10\) cm
c) radius = \(\dfrac{7}{22}\) miles
d) radius = \(4.45\) km
2) Find the circumference of a circle given the length of a diameter. Leave your answer two ways: in terms of \(\pi\) and rounded to the nearest tenth.
a) diameter = \(18\) cm
b) diameter = \(13.4\) in.
3) Find the radius of a circle give the length of the circumference. Round your answer to the nearest tenth.
a) circumference = \(9\pi\) mm
b) circumference = \(15.12\) yd.
4) Given the following radius or diameter of a circle and its arc measure, find the arc length. Leave your answer in terms of \(\pi\).
a) Circle with radius = \(6\) in. and an arc measure of \(90^{\circ}\).
b) Circle with radius = \(3\) cm and an arc measure of \(180^{\circ}\).
c) Circle with diameter = \(13.4\) ft. and an arc measure of \(215^{\circ}\).
d) Circle with diameter = \(7.3\) mm and an arc measure of \(15^{\circ}\).
1) Find the circumference of a circle given the length of a radius. Leave your answer two ways: in terms of \(\pi\) and rounded to the nearest tenth.
a) radius = \(8\) in.
b) radius = \(10\) cm
c) radius = \(\dfrac{7}{22}\) miles
d) radius = \(4.45\) km
2) Find the circumference of a circle given the length of a diameter. Leave your answer two ways: in terms of \(\pi\) and rounded to the nearest tenth.
a) diameter = \(18\) cm
b) diameter = \(13.4\) in.
3) Find the radius of a circle give the length of the circumference. Round your answer to the nearest tenth.
a) circumference = \(9\pi\) mm
b) circumference = \(15.12\) yd.
4) Given the following radius or diameter of a circle and its arc measure, find the arc length. Leave your answer in terms of \(\pi\).
a) Circle with radius = \(6\) in. and an arc measure of \(90^{\circ}\).
b) Circle with radius = \(3\) cm and an arc measure of \(180^{\circ}\).
c) Circle with diameter = \(13.4\) ft. and an arc measure of \(215^{\circ}\).
d) Circle with diameter = \(7.3\) mm and an arc measure of \(15^{\circ}\).
5) The inside lane, Lane \(1\), of a standard high school track is made of two straightaways and two semicircle turns. The straightaways are both \(84.39\) m in length and the radius of the turn is \(36.50\) m. What is the length of one lap of the track to the nearest tenth of a meter?
6) What is the distance of just one curve of a high school track for the inside lane? Round your answer to the nearest tenth of a meter. |
7) Leave answers in terms of \(\pi\) and to the nearest tenth of a foot. Given the circumference of a circle is \(12\pi\) ft.:
a) What is the arc length (distance) of a semicircle of the circle?
b) What is the arc length of one quarter (or \(90^{\circ}\)) of the circle?
c) What is the arc length of \(243^{\circ}\) of the circle?
d) What is the length of an arc that is \(\frac{1}{10}\)th of the circumference?
e) What is the length of an arc that is \(\frac{5}{6}\)th of the circumference?
a) What is the arc length (distance) of a semicircle of the circle?
b) What is the arc length of one quarter (or \(90^{\circ}\)) of the circle?
c) What is the arc length of \(243^{\circ}\) of the circle?
d) What is the length of an arc that is \(\frac{1}{10}\)th of the circumference?
e) What is the length of an arc that is \(\frac{5}{6}\)th of the circumference?
9) The measure of an arc is \(45^{\circ}\) and the arc length is \(9.42\) in. What is the circumference of the circle? Round to the nearest hundredth.
10) The measure of an arc is \(135^{\circ}\) and the arc length is \(23.56\) m. What is the circumference of the circle? Round to the nearest hundredth.
11) What fraction of the circumference is an arc length \(84\pi\) if the circumference of a circle is \(112\pi\)?
12) The two sets of colonnades around St. Peter’s Square in Vatican City are both create an arc \(160^{\circ}\) of an imaginary circle that with a diameter of \(450\) ft. What is the inside length of one of the colonnades to the nearest foot?
10) The measure of an arc is \(135^{\circ}\) and the arc length is \(23.56\) m. What is the circumference of the circle? Round to the nearest hundredth.
11) What fraction of the circumference is an arc length \(84\pi\) if the circumference of a circle is \(112\pi\)?
12) The two sets of colonnades around St. Peter’s Square in Vatican City are both create an arc \(160^{\circ}\) of an imaginary circle that with a diameter of \(450\) ft. What is the inside length of one of the colonnades to the nearest foot?
13) A company packs boxes with a product. The product enters through shipping and passes through a conveyor belt traveling four straightaways and three curves. Each curve is an arc length of a circle with a radius of \(2\) feet as shown. Finally, the product returns to shipping. What is the total length of the conveyor belt? Round to the nearest foot.