Exercises on circumference and circle are always in assessments and entrance exams. Practice with this list of exercises and solve your doubts with the solutions explained step by step.
To organize the flow of vehicles in traffic, engineers and designers often use roundabouts instead of traffic lights, a solution that can be more efficient in many cases. In a roundabout, the segment that connects the middle of the lane at two ends is 100 m. A driver completing a lap will travel
data: use =3.
a) 100 m.
b) 150 m.
c) 300 m.
d) 200 m.
The segment that connects the middle of the lane at two ends is the diameter of the roundabout.
To calculate the length of the roundabout, we use:
Where,
C is the length,
r is the radius
Since the diameter is equal to twice the radius, we have:
So the length will be:
In a complete turn, the driver will travel 300 meters.
A brake disc is a circular piece of metal that forms part of a vehicle's braking system. It has the function of delaying or stopping the rotation of the wheels.
To manufacture a batch of 500 brake discs with a diameter of 20 cm and an empty central area to attach the hub wheel, 12 cm in diameter, a manufacturer will use, in square meters, a total of sheet metal of about in:
data: use .
a) 1 m.
b) 10 m.
c) 100 meters
d) 1000
We can calculate the larger area and the smaller the central one.
The area of a circle is calculated by:
larger area
Since the diameter is 20 cm, the radius is 10 cm. In meters, 0.1 m.
central area
Disk area = larger area - smaller area
disk area =
How are 500 disks:
replacing by the value of 3.14 informed in the statement:
An amusement park is building a Ferris wheel 22 meters in diameter. A steel frame in the shape of a circle is being built to secure the seats. If each seat is 2 m away from the next and considering = 3, the maximum number of people who can play this toy at once is
a) 33.
b) 44.
c) 55.
d) 66.
First we must calculate the length of the circle.
Since the seats are spaced 2 m apart, we have:
66 / 2 = 33 seats
A bicycle is equipped with 26-inch wheels, measured in diameter. The distance traveled in meters after ten complete turns of the wheels is
1 inch = 2.54 cm
a) 6.60 m
b) 19.81 m
c) 33.02 m
d) 78.04 m
To calculate a complete turn in inches, we do:
In centimeters:
C = 78. 2.54 = 198.12 cm
In meters:
C = 1.9812 m
in ten laps
19.81 m
A club is building a circular kiosk 10 m in diameter to serve customers arriving from all directions. The ducts and plumbing have already been installed, now a 5 cm thick concrete base will be built. How many cubic meters of concrete will be needed to fill this area?
consider .
a) 3.10 m³
b) 4.30 m³
c) 7.85 m³
d) 12.26 m³
Calculating how many cubic meters will be needed, is to calculate the volume of the base.
To calculate the volume, we determine the area and multiply it by the height, in this case 10 cm.
Multiplying by the height of 10 cm or 0.1 m:
replacing by 3.14:
Planet Earth has an approximate radius of 6378 km. Suppose a ship is on a straight path moving in the Pacific Ocean between points B and C.
Taking the Earth as a perfect circle, consider that the ship's angular displacement was 30º. Under these conditions and considering = 3, the distance in kilometers traveled by the ship was
a) 1557 km
b) 2 364 km
c) 2 928 km
d) 3,189 km
1 full turn = 360 degrees
With a radius of 6 378 km, the circumference is:
Making a rule of three:
(Enem 2016) The project for afforestation of a square includes the construction of a circular flowerbed. This site will consist of a central area and a circular band around it, as shown in the figure.
You want the central area to be equal to the area of the shaded circular strip.
The relationship between the radii of the bed (R) and the central area (r) must be
a) R = 2r
b) R = r√2
w)
d)
It is)
central area
Circular band area
Since the central area must be equal to the circular shaded area:
The figure represents a circle λ with center C. Points A and B belong to the circle of λ and point P belongs to. It is known that PC = PA = k and that PB = 5, in units of length.
The area of λ, in units of area, is equal to
a) π(25 - k²)
b) π(k² + 5k)
c) π(k² + 5)
d) π(5k² + k)
e) π(5k² + 5)
Data
- CA = CB = radius
- PC = AP = k
- PB = 5
Goal: calculate the circular area.
The circular area is , where the radius is the segment CA or CB.
Since the answers are in terms of k, we must write the radius in terms of k.
Resolution
We can identify two isosceles triangles.
Since PC = PA, the triangle is isosceles, and the base angles
It is
, they are the same.
Since CA = CB, the triangle is isosceles, and the base angles
It is
, they are the same.
Thus, the two triangles are similar due to the AA (angle-angle) case.
Writing the proportion between the ratios of two similar sides, , we have:
Since we want the circular area:
(UNICAMP-2021) The figure below shows three circles tangent two by two and the three tangents to the same straight line. The radii of the larger circles have length R and the smaller circle has a radius of length r.
The R/r ratio is equal to
3.
√10.
4.
2√5.
Adjusting the radii we form a right triangle with hypotenuse R+r and legs R and R - r.
Applying the Pythagorean Theorem:
(Enem) Consider that the blocks of a neighborhood have been drawn in the Cartesian system, the origin being the intersection of the two busiest streets in that neighborhood. In this drawing, the streets have their widths disregarded and all the blocks are squares with the same area and the measure of its side is the system unit.
Below is a representation of this situation, in which points A, B, C and D represent commercial establishments in that neighborhood.
Suppose that a community radio, with a weak signal, guarantees a coverage area for every establishment located at a point whose coordinates satisfy the inequality: x² + y² – 2x – 4y - 31 ≤ 0
In order to evaluate the quality of the signal, and provide a future improvement, the technical assistance of the radio carried out an inspection to know which establishments were within the coverage area, as these can hear the radio while the others no.
a) A and C.
b) B and C.
c) B and D.
d) A, B and C.
e) B, C and D.
The circumference equation is:
The problem equation is:
The center of a circle is the point C(a, b). To determine the coordinates, we equate the coefficients of like terms.
For terms in x:
For terms in y:
The center of the circle is the point C(1, 2)
To find the radius we equate the free terms of x and y:
The radio signal will serve establishments in the area of the circumference with center C(1, 2) and radius less than or equal to 6. Marking the drawing on the plane:
Establishments A, B and C will receive the radio signal.
