202110233-TRIUMPH-STUDENT-WORKBOOK-MATHEMATICS-G08-PART1

10 [AS1] Two circles touch internally. The sum of their areas is 116 π and the distance between their centres is 6 cm. Find the radii of the circles. 11 [AS1] Two circles touch externally. The sum of their areas is 130π sq. cm and the distance between their centres is 14 cm. Find the radii of the circles. 12 [AS1] Find the area of the shaded region in the following figure. 13 [AS1] Find the area of the shaded region in the square ABCD. EXERCISE 9.2. AREA OF CIRCLE 98

14 [AS4] A steel wire, when bent in the form of a square, encloses an area of 121 sq. cm. The same wire is bent in the form of a circle. Find the area of the circle. 15 [AS4] The radii of the inner and outer boundaries of a circular park are 56 m and 70 m respectively. Find the area of the circular path. EXERCISE 9.2. AREA OF CIRCLE 99

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EXERCISE 10.3 COMPOUND PROPORTION 10.3.1 Key Concepts i. Sometimes change in one quantity depends upon the change in two or more other quantities in the same proportion. Then we equate the ratio of the first quantity to the compound ratio of the other two quantities. 10.3.2 Additional Questions Objective Questions 1. [AS3] If a change in one quantity depends upon a change in two (or) more quantities in some proportion then it is known as a/ an proportion. (A) Direct (B) Inverse (C) Compound (D) None of these 2. [AS3] ‘a’ men can lay a road of ‘b’ km in ‘c’ days. Here 'c' is in inverse proportion with ‘a’ and in proportion with ‘b’. (A) Direct (B) Inverse (C) Compound (D) None of these 3. [AS4] 100 men can construct a wall of 1000 m in 20 days. The number of days that 200 men take to construct a wall of length 1500 m is ______. (A) 30 days (B) 15 days (C)20 days (D)10 days 4. [AS4] 15 men can lay a road 300 km long in 10 days. The number of days 25 men take to lay a road 100 km long is ____. (A) 5 days (B) 20 days (C)10 days (D)2 days EXERCISE 10.3. COMPOUND PROPORTION 107

5. [AS4] 350 men can clean a road 6300 km long in 72 days. The number of men required to clean a road of 7800 km long in 48 days is ______. (A) 325 (B) 650 (C) 975 (D)None of these 6. [AS4] 15 boys earn Rs. 900 in 5 days. The amount earned by 20 boys in 7 days is _____. (A) Rs.1800 (B) Rs.1680 (C) Rs.1400 (D)Rs. 2520 Very Short Answer Type Questions 7 [AS3] Answer the following questions in one sentence. Define compound proportion. Long Answer Type Questions 8 [AS4] 32 workers working 9 hours a day can finish a piece of work in 20 days. If each worker works 6 hours a day, find the number of workers needed to finish the same piece of work in 24 days. 9 [AS1] (i) If A : B = 3 : 4 and B : C = 5 : 6, then find A : C. (ii) Find the value of the unknown. 24 : 12 :: x : 15 10 [AS5] The mess charges for 65 students for 30 days is Rs. 24,375. How much will be the mess charges for 75 students for 45 days? Represent these values in the form of a table. EXERCISE 10.3. COMPOUND PROPORTION 108

—— Project Based Questions —— (i) We can see many applications of the different properties like commutative, associative that are used in mathematics in our real life. For example : Commutative property : There were two friends Sita and Geeta. Sita had 1 of a pizza and 4 2 2 1 Geeta had 4 of the pizza. Now, if Sita took 4 more and Geeta took 4 more from the plate, then do both of them have an equal amount of pizza? This is an example where commutative property of addition for rational numbers can be applied. Create five questions related to real life scenarios where the application of different properties like associative property, distributive property can be shown. (ii) Solving a linear equation is similar to balancing a weighing scale. We add or keep removing objects till will get our desired result. We can also solve these using strips of coloured paper. Here is an example: Create a chart showing an example of solution for a linear equation using different coloured papers. Specify what each colour represents. PROJECT BASED QUESTIONS 109

(iii) You need to create a paper quilt made out of quadrilaterals. The quilt must use all of the different types of quadrilaterals that you have learnt to construct and you need to include measurements of sides and angles, that you have constructed. Here is an example of a paper quilt. (iv) The size of a planet is very big and the size of a cell is very small. Such large or small sizes are difficult to show without having a method such as scientific notation. Scientific notation is used extensively in the field of science. Research in the internet and give example of numbers which are used in the scientific field and the need to be expressed using scientific notation. Also write your numbers in standard and scientific form. Here is an example: This table shows the distance of each planet from the earth: PROJECT BASED QUESTIONS 110

Planet Standard Form (km) Scientific Notation (km) Earth 150000000 1.5 × 108 Jupiter 778000000 7.78 × 108 Mars 228000000 2.28 × 108 Mercury 58000000 5.8 × 10 Neptune 4498000000 4.498 × 109 Saturn 1427000000 1.427 × 109 Uranus 2871000000 2.871 × 109 Venus 108000000 1.08 × 108 (v) During the festival season, we observe that many sellers give us a lot of discounts. Collect information from newspapers about discounts on different products. Prepare a report showing, which is the bestseller according to the amount of discount given. Show your calculation as to how you decided who the best seller is. (vi) Using square numbers there are very interesting patterns that can be observed. For example, A B 12 = 1 1 + 3 = 4 = 22 112 = 121 1 + 3 + 5 = 9 = 32 1112 = 12321 1 + 3 + 5 + 7 = 16 = 42 Collect some number patterns which use square numbers and cube numbers. (vii) The golden ratio is a number that can be used to compare different parts of our body, from the length of the arms and legs compared to the toes. Make a table containing the following ratios: 1. Height: length between naval point and foot PROJECT BASED QUESTIONS 111

2. Length of the shoulder line: length of the head 3. Length between finger tip and elbow: length between wrist and elbow 4. Length between naval point and knee: length between knee and foot Take these measurements for a few of your friends and discover the ratio you obtain in each case. (viii) Make a list of 15 items like petrol, milk, pulses, onions etc. Find out the price of these items by asking your parents or by using internet. Find out the price of the same items 20 years ago. For each item calculate the increase or decrease percentage. Present your findings in a tabular format. (ix) PROJECT BASED QUESTIONS 112