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Areas Related to a Circle — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsAreas Related to a Circle1 Mark
MCQ
Choose the correct answer from the given four options : It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters $16m$ and $12m$ in a locality. The radius of the new park would be :
  • ✓
    $10m$
  • B
    $15m$
  • C
    $20m$
  • D
    $24m$
✓

Answer

Correct option: A.
$10m$
Area of first circular park, whose diameter is $16m$
$=\pi\text{r}^2=\pi\Big(\frac{16}{2}\Big)^2=64\pi\text{m}^2$
$\Big[\because\text{r}=\frac{\text{d}}{2}=\frac{16}{2}=8\text{m}\Big]$
Area of second circular park, whose diameter is $12m$
$=\pi\Big(\frac{12}{2}\Big)^2=\pi(6)^2=36\pi\text{m}^2$
$\Big[\because\text{r}=\frac{\text{d}}{2}=\frac{12}{2}=6\text{m}\Big]$
According to the given condition,
Area of single circular park $=$ Area of first circular park $+$ Area of second circular park
$\pi\text{R}^2=64\pi+36\pi\ [\because R$ be the radius of single circular park$]$
$\Rightarrow\ \ \pi\text{R}^2=100\pi$
$\Rightarrow\text{R}^2=100$
$\therefore\ \ \text{R}=10\text{m}$

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