Question

13. The area of two equal circles in the figure
is 308 cm?. Find the area of the rectangle.

Ans is 392

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Answer 1

Answer:

$area \: of \: circle = \pi \: r {}^{2}$

$308 \: cm \: = \frac{22}{7} \times r {}^{2}$

$\frac{308 \times 7}{22} = r {}^{2}$

$98 = r {}^{2}$

$\sqrt[2]{98} = r$

$9.89 \: cm = r$

$diameter = 2 \times r$

$diameter = 2 \times 9.89$

$= 19.78$

$diameter = breadth \: of \: rectangle$

$breadth \: of \: rectangle = 19.78 \: cm$

$length \: = sum \: of \: diameters \: of \: two \: circles$

$length \: = 19.78 + 19.78$

$= 39.56 \: cm$

$area \: of \: rectangle = l \times b$

$= 19.78 \times 39.56$

$= 782.4968 \: cm {}^{2}$

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Answer 2

Question :

The area of two equal circles in the figure

is 308 cm?. Find the area of the rectangle.

Answer :

$\sf\pink{Given:}$

• Area of two equal circles is 308 cm² .

$\sf\pink{To\:find:}$

• Area of the rectangle ?

Explanation :

To find the area of a rectangle we need to find the length and breadth of the rectangle . The length will be equal to the sum of diameter of both the circles . And the breadth will be the diameter of any one circle because they are inscribed inside the rectangle . To find the diameter we need to find the radius of the circle .

Area of both circles is 308 cm²

Area of 1 circle = $\sf{\dfrac{308}{2}}$

$\longrightarrow\sf{154}$

• Area of one of the circle is 154 cm² .

Area of circle = πr²

$\longrightarrow\sf{154 = \dfrac{22}{7}\times {r}^{2}}$

$\longrightarrow\sf{154\times \dfrac{7}{22} = {r}^{2}}$

$\longrightarrow\sf{7\times 7 = {r}^{2}}$

$\longrightarrow\sf{49 = {r}^{2}}$

$\longrightarrow\sf{r = \sqrt{49}}$

$\longrightarrow\sf{r = 7}$

• Therefore the radius is 7 cm .

Diameter = 2 × radius

$\longrightarrow\sf{2\times 7}$

$\longrightarrow\sf{14 cm}$

• Therefore the diameter is 14 cm.

Length of the rectangle = 2 × diameter

$\longrightarrow\sf{2\times 14}$

$\longrightarrow\sf{28}$

• Therefore length of the rectangle is 28 cm .

Breadth of the rectangle = diameter

$\longrightarrow\sf{14}$

• Therefore breadth of the rectangle is 14 cm .

Area of Rectangle = length × breadth

$\longrightarrow\sf{28\times 14}$

$\longrightarrow\sf{392}$

• Therefore the area of the rectangle is 392 cm²