The diagram shows a circle with centre O and radius r cm. Points A and B lie
Question:
The diagram shows a circle with centre O and radius r cm. Points A and B lie on TU the circle and angle AOB = π/4 radians. The tangent to the circle at A intersects the straight line through O and B at the point C.
a) Find expressions in terms of r for
i) The area of sector OAB
ii) The length of AC
iii) The area of triangle OAC.
The area of the shaded region is 100 cm².
b) Find the value of r.
0 rcm TU 4 A B B C
Step by Step Answer:
ANSWER a i The area of sector OAB is given by the formula A 12 r2 where is the angle in radians In t...View the full answer
Complete Pure Mathematics 1 For Cambridge International AS & A Level
ISBN: 9780198427438
2nd Edition
Authors: Jean Linsky, Brian Western, James Nicholson
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 circle with centre O and radius r cm. The points P, Q, and R lie on the circle. The line PR is a diameter of the circle and angle POQ = 2 radians. The area of sector QOR is 30 cm...
-
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...
-
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...
-
Lombard Ltd has been offered a contract for which there is available production capacity. The contract is for 20,000 identical items, manufactured by an intricate assembly operation, to be produced...
-
The following data represent the number of live multiple-delivery births in 2007 for women 15 to 54 years old. Age .....Number of Multiple Births 1519 ..... 100 20-24 ..... 467 2529 ....1620 30-34...
-
Finding the WACC given the following information for Bellevue Power Co, find the WACC. Assume the companys tax rate is 35 percent. Deb:5,000 7 percent coupon bonds outstanding, $1,000 par value, 20...
-
The armature of a variable-speed electric motor, of mass \(200 \mathrm{~kg}\), has an unbalance due to manufacturing errors. The motor is mounted on an isolator having a stiffness of \(10 \mathrm{kN}...
-
In conducting year-end inventory counts, your audit team is debating the impact of the clients right of return policy both on inventory valuation and revenue recognition. The assistant controller...
-
Lavage Rapide is a Canadian company that owns and operates a large automatic car wash facility near Montreal. The following table provides estimates concerning the company's costs: Fixed Cost Cost...
-
Below are shown three different crystallographic planes for a unit cell of some hypothetical metal. The circles represent atoms: (a) To what crystal system does the unit cell belong? (b) What would...
-
An angle is known to be between 270 and 360 and sin = 9/25 Find a) sin b) cos c) tan.
-
In the diagram, the line PQ divides the circle with centre O and radius r into two segments. Show that when angle POQ = 2.6 radians, the area of the larger segment is approximately twice the area of...
-
Draw a Feynman diagram for the reaction n + v p + .
-
What changes did the classical tort reformers bring to the tort system, and why?
-
What effects has the tort system had on the medical community?
-
True Or False The excessive fines clause of the Eighth Amendment does not apply to punitive damages, but the due process clause does.
-
Indemnification sometimes arises out of a. the laws attempt to avoid unjust enrichment of a tortfeasor. b. a contractual agreement. c. a relationship in which one party is vicariously liable for the...
-
True Or False Although individual cases may point to a dysfunctional system, they may be misleading when not all of the facts are known.
-
Ethylene glycol, HOCH2CH2OH, is used as antifreeze. It is produced from ethylene oxide, C2H4O, by the reaction C2H4O(g) + H2O(l) HOCH2CH2OH(l) Use Hesss law to obtain the enthalpy change for this...
-
Suppose you are comparing just two means. Among the possible statistics you could use is the difference in means, the MAD, or the max min (the difference between the largest mean and the smallest...
-
The average loss from robbery in the United States in 2014 (last year available) was $1,227. Suppose that an insurance analyst wanted to know whether the type of robbery differs in the years 1995,...
-
Exercise 2.34 presented the data from a Pew Research Center survey of American adults describing whether their friends share their political views. Also recorded were the political views of the...
-
In Exercise 2.35 a Gallup survey asked American adults whether they believed that upper income people are paying their fair share in federal taxes. Each respondent was also classified as 1....
-
Laramie Company has variable cost ratio of 0 . 3 5 . The fixed cost is $ 1 1 3 , 7 5 0 and 2 5 , 0 0 0 units are sold at break - even. What is the price? What is the variable cost per unit? The...
-
Analyze the accounting issues raised by the Enron case. If you knew about these facts before they became public, what, if anything, would you have done? What does this case demonstrate about the...
-
In September, Lauren Ashley Company purchased materials costing $220,000 and incurred direct labor cost of $150,000. Overhead totaled $300,000 for the month. Information on inventories was as...
Study smarter with the SolutionInn App