Question

the given figure a circle circumscribes a rectangle then the ratio of area of circle to the area of rectangle is​

Answer 1

Answer:

(c) 25π:48

Step-by-step explanation:

area of circle=πr²

diameter of circle=√(64+36)=10

radius of circle=5

hence,

area of circle=5²π =25π

area of rectangle=length×breadth

area of rectangle=6×8=48

hence ratio is

area of circle = 25π

area of rectangle 48

= 25π:48

Answer 2

Given,

The length of the rectangle$\[ = 8\]$

The breadth of the rectangle$\[ = 6\]$

To find,

The ratio of the area of the circle to the area of the rectangle.

Solution,

Apply Pythagoras theorem in the triangle ADB,

$\[ \Rightarrow BD = \sqrt {{{\left( {AB} \right)}^2} + {{\left( {AD} \right)}^2}} \]$

Apply values.

$\[\begin{array}{l} \Rightarrow BD = \sqrt {{{\left( 6 \right)}^2} + {{\left( 8 \right)}^2}} \\ \Rightarrow BD = \sqrt {36 + 64} \\ \Rightarrow BD = \sqrt {100} \\ \Rightarrow BD = 10\end{array}\]$

Know that the radius of the circle is half the diameter of the circle.

Therefore,

$\[\begin{array}{l} \Rightarrow \frac{{10}}{2}\\ \Rightarrow 5\end{array}\]$

Know that the area of the circle is given as $\[\pi {r^2}.\]$

Therefore, the area of the circle is

$\[\begin{array}{l} \Rightarrow \pi {\left( 5 \right)^2}\\ \Rightarrow 25\pi \end{array}\]$

Know that the area of a rectangle is given as $\[l \times b.\]$

Therefore, the area of the rectangle is

$\[\begin{array}{l} \Rightarrow 8 \times 6\\ \Rightarrow 48\end{array}\]$

So, the required ratio of the area of the circle to the area of the rectangle is

$\[\begin{array}{l} \Rightarrow \frac{{25\pi }}{{48}}\\ \Rightarrow 25\pi :48\end{array}\]$

Hence, the ratio of the area of the circle to the area of the rectangle is$\[25\pi :48\]$.