6.(a) Find the length of the arc that subtends an angle of measue 30° on a circle of diameter 18 cm; (b) Find the area of the sector given in part (a)

For the two circles in figures a, b, and c, find the total number of common tangents internal and external.

In order to make a conical duct, a circular sheet of metal is to be cut in the shape of a sector of a circle. If the radius of the sector is 28.5 in. and the arc length of the of the sector is 26.4 in., what are the central angle, , and area of the sector?

The oblique circular cone has an altitude and a diameter of base that are each of length 6 cm. The line segment joining the vertex to the center of the base is the axis of the cone. What is the length of the axis?

Find the perimeter of a segment of a circle whose boundaries are a chord measuring 24 mm millimetres and an arc of length 30 mm.

A metal circular disk whose area is 143 cm2 is used as a knock out opening on an electrical service in a factory. Use your calculator value of to find the length of the radius of the disk to the nearest tenth of a cm.

The larger circle is inscribed in a square with sides of length 4cm. The smaller circle is tangent to the larger circle and to two sides of the square, as shown. Find the length of the radius of the smaller circle.

The center of a circle of radius 2 inches is at a distance of 10 inches from the center of a circle of radius length 3 inches. To the nearest tenth of an inch, what is the approximate length of a common internal tangent? Use the hint provided in Exercise 38. HINT: use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice.

A goat is tethered to a barn by a 12-ft chain. If the chain is connected to the barn at a point 6 ft from one end of the barn, what is the area of the pasture that the goat is able to graze?

Determine the arc length from point C to point D on the template shown.