The diagram shows sector OAB of a circle with centre O, radius 6cm and sector angle /3
Question:
The diagram shows sector OAB of a circle with centre O, radius 6cm and sector angle π/3 radians.
The point X lies on the line OA and BX is perpendicular to OA.
a. Find the exact area of the shaded region.
b. Find the exact perimeter of the shaded region.
6 cm 0 اتانيا B X A
Step by Step Answer:
a the exact area of the shaded region A...View the full answer
Cambridge International AS And A Level Mathematics Pure Mathematics 1 Coursebook
ISBN: 9781108407144
1st Edition
Authors: Sue Pemberton, Julian Gilbey
Related Video
The area of a circle is given by the formula: A = ?r^2 Where A is the area, ? is a mathematical constant (approximately 3.14), and r is the radius of the circle. The radius is the distance from the center of the circle to the edge. So for example, if the radius of a circle is 5 units, the area would be: A = ?(5^2) = ?(25) = 78.5 square units Here three friends went out to a restaurant and decided to have pizza for lunch. While they were waiting for their order, one of them stepped out to take a call but promised to return in two minutes. The waiter came and presented them with the menu, and they decided to order two 10-inch pepperoni pizzas. The waiter took their order and left. Just then, the third friend returned and asked what they had ordered. They explained that they had ordered two small pepperoni pizzas as they were only three of them and it would be enough for them. However, the third friend suggested that for the same price, they could get a large pizza that would be much bigger than the two small ones. He asked the waiter for a pen and paper and proceeded to calculate the area of the two small pizzas and compared it to the area of one large pizza. The friends were amazed at how the circle measurements worked and decided to change their order from two small pizzas to one large pizza.
Students also viewed these Mathematics questions
-
The diagram shows a sector OAB of a circle with centre O and radius r. Angle AOB is radians. The point C on OA is such that BC is perpendicular to OA. The point D is on BC and the circular arc AD...
-
The diagram shows a sector OPQ of a circle with centre O and radius x cm. Angle POQ is 0.8 radians. The point S lies on OQ such that OS = 5 cm. The point R lies on OP such that angle ORS is a right...
-
A sector of a circle with radius 8 cm has central angle 4/7. a. Find the area of the sector. b. Set up a proportion of the area of the sector to the total area of the circle, and a proportion of the...
-
For nearly 50 years, Loganville Window Treatments (LWT) of Loganville, Georgia, has made interior shutters that are sold through decorating centers. Figure 3.20 shows some of the various styles of...
-
Determine whether each of the following statements is (i) Always true, (ii) Sometimes true, or (iii) Never true. For those that are (ii) Sometimes true, explain when the statement is true. a....
-
As worldwide air traffic volume has grown over the years, the problem of airplanes striking birds and other flying wildlife has increased dramatically. The International Journal for Traffic and...
-
An inward flow radial turbine (see Fig. P5.89) involves a nozzle angle, \(\alpha_{1}\), of \(60^{\circ}\) and an inlet rotor tip speed, \(U_{1}\), of \(6 \mathrm{~m} / \mathrm{s}\). The ratio of...
-
On 1 April year 1, a deep discount bond was issued by DDB AG. It had a face value of 2.5 million covering a five-year term. The lenders were granted a discount of 5%. The coupon rate was 10% on the...
-
Net Zero Products, a wholesaler of sustainable raw materials, prepares the following aging of receivables analysis. Accounts receivable Percent uncollectible Total $ 153,500 0 $ 91,000 1 to 30 $...
-
Renee is considering the purchase of an annuity with half of her RRSP funds. Renee has been told that for $145000 she could receive a no guarantee life annuity based on her single life that pays...
-
a. Find the first three terms in the expansion of (3 2x) 7 , in ascending powers of x. b. Find the coefficient of x 2 in the expansion of (1 + 5x)(3 2x) 7 .
-
The graph of y = x 3 3 is transformed by applying a translation of followed by a reflection in the x-axis. Find the equation of the resulting graph in the form y = ax 3 + bx 2 + cx + d. 2 0
-
Use a two-element, finite-element model to approximate the two lowest natural frequencies of transverse vibration of the beam of Figure P11.18. -L FIGURE P11.18 E, I, p, A
-
The $7,800 has already been spent or committed. What does the relevant income or loss represent for Flagstone?
-
The mean outstanding credit card balance distributed normally for young American couples is u = $650 with a standard deviation = $420. In a simple random sample of 100 couples, what is the...
-
What series of payments is represented by the present value A.Q B-(Da)n?
-
If your company recently received items it ordered from a vendor, and the bill will arrive in one week's time, what can you do in QuickBooks to keep your records the most up-to-date?
-
Given the following data for Hometown Clinic, calculate the efficiency variance for supplies, noting if the variance is favorable or (unfavorable): 2021 2020 Supply kits used 27,900 29,715 Cost per...
-
Given that the firm did not have any problem paying the higher bill, would Nathan's planned course of action be ethical? Why or why not?
-
As economic conditions change, how do banks adjust their asset portfolio?
-
Perform the test in Problem 9.11, and report a p-value?
-
What hypotheses are being tested here? Otolaryngology, Pediatrics A common symptom of otitis media in young children is the prolonged presence of fluid in the middle ear, known as middle-ear...
-
Why might a nonparametric test be useful in testing the hypotheses? Otolaryngology, Pediatrics A common symptom of otitis media in young children is the prolonged presence of fluid in the middle ear,...
-
Calculate the sum of the cross products for the following dataset. The standard deviation of the y variable is s-3.162: x y z_score_x z_score_y 5 3 -0.75 -0.32 7 2 0.08 -0.63 4 1 -1.17 8 5 0.50 10 6...
-
Calculate the mean for this frequency distribution: Boundaries Frequency 20.5-25.5 4 25.5-30.5 10 30.5-35.5 9 35.5-40.5 5 40.5-45.5 13 (Roundup to two decimal digits)
-
2. The table below shows ages of 16 students sampled from CHEM 2010 class. a. Find the five-number summary. b. Find the modal observation(s). c. Compute and interpret the z-score of a student with...
Study smarter with the SolutionInn App