question_answer

DIRECTIONS: Passage ? 1 Read the passage(s) given below and answer the questions that follow Area between two concentric circles. Two circles are said to be concentric if they have a common center. Sometimes, we have to find the area between two concentric circles. For example, the area of a ring, the area of a circular field having a circular pond in the middle. So, let us consider two concentric circles with r as the radius of the inner circle and R as the radius of the outer circle. Area between the circles \[=\] Area of outer circle\[-\]Area of the inner circle \[=\pi {{R}^{2}}-\pi {{r}^{2}}=\pi ({{R}^{2}}-{{r}^{2}})\] A 7m wide path is to be constructed all around, and outside a circular garden of diameter 112m. The cost of constructing the path at Rs. 50 per square meter is

A) Rs. 13090                   

B) Rs. 130900

C) Rs. 1309        

D) Rs. 13000

Correct Answer: B

Solution :

    Radius of inner circle =\[\frac{112}{2}\]= 56 m Radius of outer circle = 63 m Area of path = Area of outer circle ? Area of inner circle \[=\pi \left[ {{(63)}^{2}}-{{(56)}^{2}} \right]=\frac{22}{7}\times 119\times 7\] \[=2618\,{{m}^{2}}.\] Cost of constructing the path at Rs. per sq. m \[=~2618\times 50=Rs.\,\,130900\]