10th Class Mathematics Areas Related to Circles Question Bank Case Based (MCQs) - Areas Related to Circles

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    Study Case : Q. 1 to 5
    We all love to eat pizzas, especially kids. And a variety of pizzas are available in India which have been modified according to Indian taste and menu. From the Greeks to the Egyptians, from the Persians to the Indians, there have been incarnations of pizza served throughout history, Flatbreads, naan, and plakountos are all early preparations that could be considered cousins to the modem pizza, but there isn't a consensus as to which is first and whether these could even be considered precursors to pizza at all.
    Consider two pizzas, both of equal diameter, namely, 12 inches. The first pizza marked (i) has been cut into equal slices, whereas the second pizza, marked (ii) has been cut into eight equal slices.        
    Based on the above information, answer the following questions.                                             
    The area of one slice in pizza, marked (I), is:

    A) \[6\pi \,sq.\] inches

    B) \[8\pi \,sq.\] inches

    C) \[10\pi \,sq.\] inches

    D) None of these

    Correct Answer: A

    Solution :

    We have.                                            
    Area of sector of a circle \[=\frac{\theta }{360{}^\circ }\times \pi {{r}^{2}}\]where \[\theta \] is the angle subtended by the sector at the centre.
    The radius of pizza \[(I)=6\]inches and as the pizza has been cut into six equal slices, the angle 9 subtended at the centre is equal \[\frac{360{}^\circ }{6}\]i.e., to \[60{}^\circ \].
    Required are \[=\frac{60}{360{}^\circ }\times \pi \times {{6}^{2}}=6\pi sq.\] inches.
    So, option [a] is correct.

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