MCQ
Choose the correct answer from the given four options : The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii $24\ cm$ and $7\ cm$ is :
- A$31\ cm$
- B$25\ cm$
- C$62\ cm$
- ✓$50\ cm$
✓
Answer
Correct option: D.
$50\ cm$
Let $r_1= 24\ cm$ and $r_2= 7\ cm$
$\therefore$ Area of first circle $=\pi\text{r}^2_1=\pi(24)^2=576\pi\text{ cm}^2$
and area of second circle $=\pi\text{r}^2_1=\pi(7)^2=79\pi\text{ cm}^2$
According to the given condition,
Area of circle $=$ Area of first circle $+$ Area of second circle
$\therefore\ \ \pi\text{R}^2=576\pi+49\pi \ [$where, $R$ be radius of circle$]$
$\Rightarrow\ \ \text{R}^2=625$
$\Rightarrow\ \text{R}=25\text{ cm}$
$\therefore$ Diameter of a circle $= 2R = 2 \times 25 = 50\ cm$
$\therefore$ Area of first circle $=\pi\text{r}^2_1=\pi(24)^2=576\pi\text{ cm}^2$
and area of second circle $=\pi\text{r}^2_1=\pi(7)^2=79\pi\text{ cm}^2$
According to the given condition,
Area of circle $=$ Area of first circle $+$ Area of second circle
$\therefore\ \ \pi\text{R}^2=576\pi+49\pi \ [$where, $R$ be radius of circle$]$
$\Rightarrow\ \ \text{R}^2=625$
$\Rightarrow\ \text{R}=25\text{ cm}$
$\therefore$ Diameter of a circle $= 2R = 2 \times 25 = 50\ cm$
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