question_answer

 

Directions:  Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below.

Assertion The area of the flower bed (with semi-circular ends) shown in figure.

is \[\left( 380+50\pi  \right)c{{m}^{2}}\]

Reason Area of the semi-circle is \[\frac{\pi {{r}^{2}}}{2}\]and area of rectangle is length \[\times \]breadth.

A) A is true, R is true; R is a correct explanation for A.

B) A is true, R is true; R is not a correct explanation for A.

C) A is true; R is false.

D) A is false; R is true.

Correct Answer: D

Solution :

Length and breadth of a circular bed are 38 cm and 10 cm. \[\therefore \] Area of rectangle ACDF = Length \[\times \] Breadth \[=38\times 10=380\text{ }c{{m}^{2}}\] Both ends of flower bed are semi-circles. \[\therefore \]Radius of semi-circle \[=\frac{DF}{2}=\frac{10}{2}=5\,cm\] \[\therefore \]Area of one semi-circles \[=\frac{\pi {{r}^{2}}}{2}=\frac{\pi }{2}{{\left( 5 \right)}^{2}}=\frac{25\pi }{2}c{{m}^{2}}\] \[\therefore \]Area of two semi-circles \[=2\times \frac{25}{2}\pi =25\pi c{{m}^{2}}\] \[\therefore \]Total area of flower bed = Area of rectangle ACDF + Area of two semi-circles \[=\left( 380+25\pi  \right)c{{m}^{2}}\].