Practice problems of the annulusAn annulus is a ring-shaped object, a region bounded by two concentric circles. It is a set of points whose distance from the center of S is between r1 and r2 inclusive, where r1, and r2 are radii. The area of an annulus is the difference in the areas of the larger circle of radius R and the smaller one of radius r
Direction: Solve each problem carefully and show your solution in each item.
Number of problems found: 44
- Function 59513
Expand the function f (z) into the Laurent series at point z0 for the given annulus f (z) = 1 / ((z-2) * (z-3)) a) z0 = 2, 0 3
- Concentric circles
There is given a Circle K with a radius r = 8 cm. How large must a radius have a smaller concentric circle that divides the circle K into two parts with the same area?
- Concentric 6751
A circle K with radius r = 8 cm is given. How big a radius must a smaller concentric circle divides a circle K into two parts with the same area?
- Pipe cross section
The pipe has an outside diameter of 1100 mm, and the pipe wall is 100 mm thick. Calculate the cross-section of this pipe.
Two concentric circles form an annulus of a width of 10 cm. The radius of the smaller circle is 20 cm. Calculate the area of the annulus.
The probability that a good shooter hits the center of the target circle No. I is 0.1. The probability that the target hit the inner circle II is 0.58. What is the probability that it hits the target circle I or II?
- The pipe
The pipe is 1.5 m long. Its outer diameter is 60 cm, inner diameter is 52 cm. Calculate the pipe's weight if the material's density from which it is made is 2 g/cm³. Please round the results to whole kilograms.
- Reinforcement 42491
The concrete ring (used for reinforcement in wells) has an inner diameter of 800 mm and an outer diameter of 900 mm. It is made of concrete with a density of 2,500 kg/m³. Its height is 1 m. Calculate its mass.
Calculate the area of two circles annulus k1 (S, 3 cm) and k2 (S, 5 cm).
- Pipe thickness
The outer circumference of the tube is 32cm. Its length is 60cm, density 8.5g/cm³ and weight 9.495kg. Calculate the wall thickness of the pipe.
The radius of the larger circle is 8cm, and the radius of the smaller is 5cm. Calculate the area of the annulus.
- Brass sphere
Find the weight of a brass ball with an outer radius of 12 cm and a wall thickness of 20 mm if the brass's density is 8.5 g/cm³.
- Calculate 8891
Calculate the weight of a PVC pipe with an inner diameter d = 45 mm and a length l = 3 m if the wall thickness of the pipe is s = 7.5 mm. The density of PVC is ρ = 1350 kg/m³.
- Tablecloth's 28511
The round tabletop has a capacity of 2.01 m². Calculate the round tablecloth's diameter if it exceeds the table's edge by 25 cm.
- Two annuluses
The area of the annular circle formed by two circles with a common center is 100 cm². The radius of the outer circle is equal to twice the radius of the inner circle. Determine the outside circle radius in centimeters.
- Round skirt
The cut on the round skirt has the shape of an annulus. Determine how much m² of fabric will be consumed on an 80 cm long skirt. The waist circumference is a circle with a smaller radius of 69 cm.
- Concentric 18343
Construct three concentric circles k, l, m with center at point S and with radii 2cm, 3cm, and 40mm
- Annulus from triangle
Calculate the area of the area bounded by a circle circumscribed and a circle inscribed by a triangle with sides a = 25mm, b = 29mm, c = 36mm
- Determine 12331
An annulus with an area S = 4.2 square meters has an inner radius r = 2.25 m. Determine the outer radius of the annulus.
- Concrete pipe
How much will it cost to cover a 6 m long concrete pipe with an outer radius of 1.5 m and an inner radius of 0.8 meters if one m² paint costs 24 €?
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