Circle Questions and Answers

MAKING AN ARGUMENT Your friend measures the circumference of a fitness ball as 2.04 meters and says, "The volume of t ball is 0.1433638009 cubic meters." Do you agree with your friend's statement?

Calculate the arc length S and area A of the following sector. a = 70° r = 40 cm S= cm (Round to the nearest whole number as needed.) A = cm² (Round to the nearest whole number as needed.)

A certain circle can be represented by the following equation. x² + y² + 4x - 18y + 81 = 0 What is the center of this circle ? What is the radius of this circle ?

Given the ends of the diameter of a circle at (-3,11) and (3,-13), what is the standard form of the equation of the circle? Ox² + (y - 3)2 = 153 ○ (x-4)² + (y + 3)² = 125 x² + (y - 3)² = 13

Select the standard form of the equation x2 + 8x + y² + 5y - 2 = 0 (x+4)² + (y + 2.5)² = 24.25 (x-4)² + (y-2.5)² = 24.25 (+4)² + (y + 2.5)² = 12.13 (x-4)² + (y-2.5)² = 12.13

Circle P is defined by the equation (x-4)² + (y + 3)² = 49. Which of the following shows the location of the center of Circle P and the radius of this circle? P is located at (4, -3) with a radius of 7 units P is located at (-4, 3) with a radius of 7 units P is located at (4, -3) with a radius of 49 units P is located at (-4, 3) with a radius of 49 units

When completing the square to find the standard form of the equation of the following circle, what is the center and radius of the circle? List answer as an ordered triple (x, y, r). x² + 8x + y² + 5y - 2 = 0

What is the square of radius of a circle that has a center of (3, 3) and goes through the point (1, 1) The square of the radius is type your answer...

Lucas is walking on a circular path. ed by the equation (x + 6)2 + (y- 5)2 = 36, and Neal is walking on another circular path modeled by the equation (x-9)2 + (y- 5)² = 81, where their distances are given in meters. What is the maximum distance between the walkers at any given time? 15 meters 20 meters 25 meters 30 meters

An oil slick is expanding as a circle. The radius of the circle is initially 2 meters and increases at the rate of 20 meters per day. Express the area of the circle as a function of t, the number of days elapsed. The area of a circle is A(r) = πr². (Type "pi" for the symbol π.)

Given the following equation of a circle in general form, find the equation in standard form by completing the 3x² + 30x+3y² — 12y + 12 = 0 1 Select the correct answer below: O(x-2)2 + (y + 5)² = 6² O(x - 5)² + (y + 2)² = 5² O(x + 2)2 + (y – 5)² = 5² O (x + 5)2 + (y-2)² = 6² O (x + 5)2 + (y + 2)² = 6² O (x + 5)2 + (y-2)² = 5² square.

Analyze the equation; that is, find the center, foci, and vertices of the ellipse. Graph the equation. 36x² + y² +12y = 0

Find the equation x2 + y2 + DX + Ey + F = 0 of the circle that passes through the points. To verify your result, use a graphing utility to plot the points and graph the circle. (0, 0), (0, -2), (3, 0)

What is the center and radius of the circle? (x − 3)² + (y- 5)² = 4 (3, 5); r = 2 (-3,-5); r = 4 (3, 5); r = 1 (-5, -3); r = 2

The circle x² + y² + 10x - 14y + 38 = 0 is translated one unit right and two units down. Which is the radius and center of the translated circle? Center (-4, 5); r = 6 Center (-4, 5); r = 36 Center (-5, 7); r = 6 Center (-5, 7); r = 36

Your neighbor Sally wants to plant flowers around the edge of her circular above ground pool. If the diameter of Sally's pool is 18 ft., how many feet of flowers will Sally need to plant to surround the pool? Your answer should be a number only. Use 3.14 for pi. Round your answer the nearest hundredth.

Rewrite the equation for this circle in Standard Form: x² + 14x + y² + 16y + 77 = 0 Remember. The standard form for a circle is (x - H)^2 + (y - K)² = R².

A plane intersects one nappe of a double-napped cone such that it is perpendicular to the vertical axis of the cone. Which conic section is formed? O hyperbola O ellipse O circle O parabola

A circle has a radius of 19 ft. Find the radian measure of the central angle that intercepts an arc of length 4 ft, 0 Do not round any intermediate computations, and round your answer to the nearest tenth. E radians x 3 ?

The equation of a circle is ( x + 10)²+ (y-4)² = 100. What is the center and radius of the circle? center:(10, — 4); radius: 10,000 center: (-10, 4); radius: 10 center:(10, — 4); radius: 10 center:(-10, — 4); radius: 10,000

The equation of a circle in general form is x² + y² + 18x-36y + 369 = 0 What is the equation of the circle in standard form? (x + 9)² + (y - 18)² = 36 (x + 9)² + (y - 18)² = 81 (x + 18)² + (y - 36)² = 36 (x + 18)² + (y - 36)² = 81

The size of a cell is typically found by capturing an image under a microscope then using software to measure its diameter. Two cells are measured using this method: Cell K: 9.97 x 10-3 centimeters Cell M: 4.2 x 10-4 centimeters How many times larger is the diameter of cell K than the diameter of cell M? Write your answer in standard notation, rounding to the nearest tenth.

Write the standard form of the equation of the circle with the given center and radius. Center (3,-4), r= √/7 The equation of the circle in standard form is (Simplify your answer.)

Find the standard form of the equation for the circle with the following properties. Center (-3,-1) and tangent to the y-axis

Let ABCD be a convex quadrilateral, I1 and I₂ be the incenters of ΔABC and ΔDBC respectively. The line I1I₂ intersects the lines AB and DC at the points E and F respectively. Suppose lines AB and DC intersect at P, and PE = PF. Prove that the points A, B, C, D are concyclic.

What are the center and the radius of the circle who has diameter endpoints at (-1,1) and (14, 18)? O Center: (13/2,19/2) Radius: 541 O Center: (3,6) Radius: 514 Center: (4,5) Radius: 3√5 Center: (13/2, 19/2) √514 Radius:

A simple dart target has two concentric circles. The larger circle has a radius of 4. The smaller circle has a radius of 2. The scoring should correspond to the relative difficulty of hitting the inner circle and the outer ring. How many more points should a player receive for landing a dart in the inner circle, as opposed to the outer ring? The player should receive 47 times as many points. The player should receive 2 times as many points. The player should receive 9 times as many points. The player should receive 3 times as many points.

Let O be the circumcircle of a triangle ABC. Let w be the circle tangent to BC, CA, AB at points D, E, F, respectively, such that A and w are on different sides of BC. Prove that if the radiuses of the circumcircle of the triangle ABC and w are equal, then the line OD is perpendicular to the line EF.

Write the standard form equation for the circle whose center is at (-2, 3) and that is tangent to the line 20x-21y-42 = 0. x²-4x+y² +6y-12 = 0 x² + 4x + y²-6y-12 = 0 x²-4x+y²-6y-25= 0

A circle of radius 24 units is divided into 8 congruent slices. Answer the following. SHOW WORK!! a. What is the area of each slice? b. What is the arc length of each slice? c. What is the measure of the central angle of each slice in degrees? d. What is the measure of the central angle of each slice in radians?

The long chord of a compound curve is equal to 250 meters. The PC of this curve is at Sta 10+000 and the PCC is at 10+139.393. The angle that the chord connecting the PC and PCC makes with the tangent passing through PC is equal to 4 degrees. Assuming that the common tangent is parallel to the long chord, Evaluate the Radius R1 and R2

s denotes the length of the arc of a circle of radius r subtended by the central angle θ. Find the missing quantity. 0= 1/3 radian, s = 5 feet, r = ?

The radius of a circle is 3 centimeters. What is the circle's area? Use 3.14 for π.

Find the arc lengths from P to Q if the radius r is 30.5 feet and the arc spans an angle of θ=80.14°. Round s to 2 decimal places.

The standard form for the equation of the circle with center (-3,7) and radius 4 is (x + 3)² + (y-7)² = 2 (x + 3)² + (y-7)² = 16 (x-3)²+(y + 7)2 = 16 (x-3)²+(y-7)² = 4 (x+3)² + (y-7)² = 4

The Astrodome in Houston is circular and has a circumference of approximately 2230 feet. What is the approximate diameter of the Astrodome? about 27 feet about 355 feet about 710 feet about 7,006 feet

A man bought a trampoline for his children to use. The trampoline has a diameter of 23 feet. If a man wishes to put up netting to go around the outside of the trampoline, how many feet of netting does he need? Give the exact circumference of the trampoline and then an approximation. Use ≈ 3.14. The exact circumference of the trampoline is (Type an exact answer, using as needed.) The approximate circumference the trampoline is (Type an integer or a decimal rounded to the nearest hundredth.)

Consider two concentric circles of radius 17 and 19. The larger circle has a chord, half of which lies inside the smaller circle. What is the length of the chord in the larger circle? (A) 12√2 (B) 10√3 (C) √17-19 (D) 18 (E) 8√6

A teacher is assembling 25 craft kits for her students. Each kit includes three curved pieces of wire, each corresponding to a 60° circular arc. Two pieces have a radius of 1 centimeter, and the third has a radius of 2 centimeters. What is the total length of wire that will be used to make the kits? 79.5 centimeters 104.7 centimeters 366.5 centimeters 628.3 centimeters

Given circle V with diameter TU and radius VR. RS is tangent to V at R. If VR = 17 and RS = 48, solve for VS. Round your answer to the nearest tenth if necessary. If the answer cannot be determined, click "Cannot be determined."

a) Write the equation of a circle that has diameter endpoints at (16,4) and (-12, 4). b) Write the equation of a circle that has the same center, but a radius that is twice as large as the equation you have above.

We will say that four circles have an intersection point at point P if at least two of the circles intersect at P. What is the greatest possi- ble number of intersection points of four circles of different sizes?

Which measurement is closest to the area of two pieces of pieces of pizza if the pie is 14 inches in diameter? 49/3 π square inches 28/3 π square inches 14/3 π square inches 49/6 π square inches

Find the equation of a circle where the endpoints of the diameter are (-2,3) and (12,-5). (r 5)² + (y + 1)² = 13 (+ 5)² + (y-1)² = 13 (-5)² + (y + 1)² = 65 (+ 5)2 + (y-1)² = √65

Find the Standard Form of the equation of the circle by completing the square. 8x + 32y + y² = -263 - x² Select the center and the length of radius for the circle. (-1,-5) (-3, 5) (-4, -16) r = 3 r = 4 r=6

65. The center of the inscribed circles of a triangle has been established. Which point on one of the sides of the triangle should be chosen to set the width of the compass? A. Intersections of the side and the median to that B.Intersection of the side and the angle bisector of the opposite angle C.Intersection of the side and the perpendicular passing through the center D. Intersection of the side and the altitude dropped from the opposite vertex.

The central angle of a sector is 72° and the sector has an area of 57. Find the radius. Round to the nearest tenth

In Freeport, Illinois, Empire Street runs east to west and route 26 runs north to south. Zippy's Pizza parlor is located on route 26, 3 miles south of Empire street. Zippy's advertises that it delivers within a 4 mile radius. 1. Write an equation that represents the radius of delivery for Zippy's Pizza. Assume that Zippy's is located at the origin. 2. How far east and west from route 26 can you live on Empire street and still receive Zippy's Pizza delivery? 3. Little Cubs Field is located 2 miles west and 4 miles north of Zippy's. How far is Little Cubs Field from Zippy's? 4. How far is Little Cubs Field from the radius of delivery?

Let P be any point on the curve S = 0 such that tangents from P to x² + y2 - 2x - 4y -4 = 0 makes 60° with each other and from point Q perpendicular tangents are drawn to S then Locus of P is a circle of radius 2√3 Locus of P is a circle of radius 6 Locus of Q is a circle of radius 3√2 Locus of Q is a circle of radius 6√2

A circle has a radius of 6 inches and a central angle of 60°. What is the measure of the arc length associated with this angle? OA 67 inches OB. 7 inches OC. 37 inches OD. 27 inches