In the diagram, AB is an arc of a circle with centre O and radius 4cm. Angle
Question:
In the diagram, AB is an arc of a circle with centre O and radius 4cm.
Angle AOB is α radians. The point D on OB is such that AD is perpendicular to OB.
The arc DC, with centre O, meets OA at C.
i. Find an expression in terms of α for the perimeter of the shaded region ABDC.
ii. For the case where
find the area of the shaded region ABDC, giving your answer in the form kπ , where k is a constant to be determined.
0 arad 4cm с D B
Step by Step Answer:
i To find an expression for the perimeter of the shaded region ABDC we need to find the lengths of t...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 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...
-
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 circle with centre O and a chord AB. The radius of the circle is 12 cm and angle AOB is 1.4 radians. a. Find the perimeter of the shaded region. b. Find the area of the shaded...
-
Which of the following domains are closed and which are bounded? (a) {(x, y) R: x + y 1} (b) {(x, y) = R: x + y <1} (c) {(x, y) = R: x 0} (d) {(x, y) R: x > 0, y > 0} (e) {(x, y) = R: 1 x 4,5 y 10}...
-
The Women Physicians Congress compiles data on medical school faculty and publishes the results in AAMC Faculty Roster. The following table presents a frequency distribution of rank for medical...
-
What is the decision likely to be for values of 2obt close to 0?
-
The following transactions were undertaken by Voyager Ltd during the financial year ended 30 June 2024 (ignore GST): 1. Took out a new long term loan, \($1\)000000. 2. Purchased a building to be held...
-
From an economic point of view, India and China are somewhat similar: Both are huge, low-wage countries, probably with similar patterns of comparative advantage, which until recently were relatively...
-
Explain the difference between the Energy law of Thermodynamics and Bernouli's Law in phase 1 and 2 flow. and also explain the flow that uses the above formula. draw the flow and formula, give an...
-
SMOLIRA GOLF, INCORPORATED Balance Sheets as of December 31. 2021 and 2022 Assets 2021 2022 Current assets Cash $6,358 $7,866 Accounts receivable 9248. 11,445 Inventory. 14,580 29,641 Total $30,186...
-
The diagram shows a semicircle, centre O, with radius 8cm. FH is the arc of a circle, centre E. Find the area of: a. Triangle EOF b. Sector FOG c. Sector FEH d. The shaded region. E 2 rad 0 HG
-
ABCD is a rectangle with AB = 5 cm and BC = 24 cm. O is the midpoint of BC. OAED is a sector of a circle, centre O. Find: a. The length of AO b. Angle AOD, in radians c. The perimeter of the shaded...
-
Tom owns and operates a minimart. Which of Toms actions described below are business transactions? Explain why any other actions are not considered transactions. 1. Tom reduces the price of a gallon...
-
I need to make this code read a .xml file. I created the .xml file in word and saved it as a .xml file. I put it in the corresponding NetBeans Project File but it keeps showing errors when I run it....
-
Use Figure 2.1 to justify the assumption that a typical bacterial cell (that is, E. coli ) has a surface area of 6 m2 and a volume of 1m3. Also, express this volume in Femtoliters. Make a...
-
WalkingPad is developing an aggregate plan for its folding treadmills. The company has collected the following key inputs in Table 1. Table 1 Parameter Hiring Cost per unit Layoff Cost per unit Cost...
-
Resource: Brochure Builder Choose a federal environmental law or policy. Create a tri- or bi-fold brochure addressing the following: Describe the chosen federal environmental law or policy. Explain...
-
4. (3 pts) Which numbered hydrogen has the lowest pKa? Explain your answer in words and by using structures. 4 1 H H- H SP3 IN H 2 SP 3 I w H Spa Sp3 HH 5
-
Prepare a metes-and-bounds description for the property shown in the accompanying figure. Assume all corners are marked with 2-in.-diameter iron pipes. East 299.3? NW Cor. Sec. 17 T7N, R8E, 4 P 4...
-
The population of Detroit, Michigan, decreased from 1,027,974 in 1990 to 688,701 in 2013 (Source: U.S. Census Bureau). Find the average rate of change in the population of Detroit, Michigan, over the...
-
a. Find where a is a positive constant. b. Hence find the value of S (4e-* + Se-x) dx,
-
The points P(1, 2) and Q(2, k) lie on the curve for which dy/dx =3 - 2/x. The tangents to the curve at the points P and Q intersect at the point R. Find the coordinates of R.
-
a. Find b. Show that [4e* (3 + ex) dx.
-
a) Stock A is expected to provide a dividend of $10 a share forever (starting next year); b) Stock B is expected to pay a dividend of $5 next year. Thereafter, dividend growth is expected to be 4%...
-
Suppose there were an alternative replacement machine that could do the same job as the new stamping machine under your consideration in Question 1. The alternate choice offers the following...
-
Elternteil Corporation owns 70 percent of Schwester Corporation's common stock and 45 percent of Bruder Corporation's common stock. In addition, Schwester owns 40 percent of Bruder's stock. In 20X6,...
Study smarter with the SolutionInn App