Q26 of 9 Page 1

In the figure, quadrilateral ABCD is circumscribing a circle with centre O and AD ⊥ AB. If radius of incircle is 10cm, then the value of x is.


A = OPA = OSA = 90°


Hence, SOP = 90°


Also, AP = AS (Tangents from an external point are equal)


Hence, OSAP is a square


AP = AS = 10cm


CR = CQ = 27cm


BQ = BC – CQ = 38 – 27 = 11cm


BP = BQ = 11 cm


x = AB = AP + BP = 10 + 11 = 21 cm


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18

Case Study Based- 2

SCALE FACTOR AND SIMILARITY


SCALE FACTOR


A scale drawing of an object is the same shape as the object but a different size.


The scale of a drawing is a comparison of the length used on a drawing to the length it represents. The scale is written as a ratio.


SIMILAR FIGURES


The ratio of two corresponding sides in similar figures is called the scale factor.


Scale factor = length in image / corresponding length in object


If one shape can become another using Resizing then the shapes are Similar.



Rotation or Turn



Reflection or Flip



Translation or Slide



Hence, two shapes are Similar when one can become the other after a resize, flip, slide or turn.


(a) A model of a boat is made on the scale of 1:4. The model is 120cm long. The full size of the boat has a width of 60cm. What is the width of the scale model?



(i) 20 cm (ii) 25 cm (iii) 15 cm (iv)240 cm


(b) What will affect the similarity of any two polygons?


(i) They are flipped horizontally


(ii)They are dilated by a scale factor


(iii)They are translated down


(iv)They are not the mirror image of one another


(c) If two similar triangles have a scale factor of a: b. Which statement regarding the two triangles is true?


(i)The ratio of their perimeters is 3a : b


(ii)Their altitudes have a ratio a:b


(iii)Their medians have a ratio 20

Case Study Based- 4

100m RACE



A stopwatch was used to find the time that it took a group of students to run 100 m.



(a) Estimate the mean time taken by a student to finish the race.


(i)54


(ii)63


(iii)43


(iv)50


(b) What will be the upper limit of the modal class?


(i)20


(ii)40


(iii)60


(iv)80


(c) The construction of cumulative frequency table is useful in determining the


(i)Mean


(ii)Median


(iii)Mode


(iv)All of the above


(d) The sum of lower limits of median class and modal class is


(i)60


(ii)100


(iii)80


(iv)140


(e) How many students finished the race within 1 minute?


(i)18


(ii)37


(iii)31


(iv)8


 23

Find a quadratic polynomial whose zeroes are 5-3√2 and 5+3√2.

 35

Water is flowing through a cylindrical pipe of internal diameter 2cm, into a cylindrical tank of base radius 40 cm at the rate of 0.7m/sec. By how much will the water rise in the tank in half an hour?