Question

find the circumstance of the circle whose area is 36times the area of circle with diameter 10.5cm.



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Answer 1

Answer:

${\boxed{\rm{Circumference =198\: cm \: \: [Approx.] }}}$

Step-by-step explanation:

Given that,

• Area is 36 times of the area of a circle with diameter 10.5 cm
• Circumference = ?

Formula used:-

${\boxed{\bold\green{Area\:of\:circle=\pi {r}^{2} }}}$

${\boxed{\bold\purple{Circumference = 2\pi r }}}$

$\tt Radius =\frac{diameter}{2} \\\rightarrow\tt Radius = \frac{10.5}{2} \\\rightarrow{\boxed{\bold\red{Radius = 5.25\: cm}}}$

$\tt According\:to\:question:-$

$\rightarrow\rm Area_1 =36 \times Area_2 \\\rightarrow\rm Area_1 = 36\times \pi \times {5.25}^{2} \\\rightarrow\rm Area_1 = 36 \times 3.1416 \times 27.5625 \\\rightarrow{\boxed{\bold\green {Area_1 = 3118 \:{cm}^{2} }}}$

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$\rm Now, 3118 = 3.1416 \times {r}^{2} \\\rightarrow\rm {r}^{2} = \frac{3118}{3.1416} \\\rightarrow\rm {r}^{2} = 992.5\:cm \\\rightarrow\rm r =\sqrt{992.5}\:cm \\\rightarrow{\boxed{\bold\green{ r = 31.5\:cm \: \: [Approx.]}}}$

$\rm So, circumference = 2\pi r \\\rightarrow\rm Circumference = 2 \times 3.1416 \times 31.5 \\\rightarrow{\boxed{\bold\purple {Circumference = 198 \:cm \: \: \: [Approx.]}}}$

Answer 2

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION \: \: } \mid}}}}}$

FORMULA USED :-

$\boxed{\red{\bold{\: Area \: \: of \: \: a \: \: circle \: = \pi \: r {}^{2}}}}$

$\boxed{\red{\bold{\: Area \: \: of \: \: a \: \: circle \: = 2 \: \pi \: r }}}$

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$\underline{ \mathfrak{ \: \: Given, \: \: }} \\ \\ \mathtt{Diameter \: \: of \: \: the \: \: first \: \: circle, d_1 = 10.5 cm} \\ \\ \mathtt{ \therefore \: Radius \: \: of \: \: the \: \: first \: \: circle, r_1 = \frac{10.5}{2} } \\ \\ \mathtt{ \therefore \: \: Area \: \: of \: \: the \: \: first \: \: circle, A_1 = \pi \: (r_1) {}^{2} } \\ \\ \mathtt{ = \frac{22}{7} \times ( \frac{10.5}{2} ) {}^{2} \: \: cm {}^{2} } \\ \\ \mathtt{ = \frac{22}{7} \times \frac{110.25}{4} \: cm {}^{2} } \\ \\ \mathtt{ = \frac{2,425.5}{28} \: \: cm {}^{2} } \\ \\ \mathtt{ = 86.625 \: \: cm {}^{2} } \:$

$\underline{ \mathfrak{ \: \: Suppose, \: \: }} \\ \\ \mathtt{The \: radius \: \: of \: \: the \: \: second \: \: circle = r_2}</p><p></p><p></p><p></p><p>$

$\mathtt{ \therefore \: \: Area \: \: of \: \: the \: \: second \: \: circle = 36 \: \: times \: \: of \: \: } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \mathtt{the \: \: area \: \: of \: \: the \: \: first \: \: circle} \\ \\ \mathtt{ \: \: \Longrightarrow \: A_2=36 \times A_1} \\ \\ \mathtt{ \: \: \Longrightarrow \: A_2=36 \times 86.625} \\ \\ \mathtt{ \: \: \Longrightarrow \: A_2=3118.5} \\ \\ \mathtt{ \: \: \Longrightarrow \: \pi \: (r_2) {}^{2} = 3118.5 } \\ \\ \mathtt{ \: \: \Longrightarrow \: \frac{22}{7} \times \: (r_2) {}^{2} = 3118.5 } \\ \\ \mathtt{ \: \: \Longrightarrow \: (r_2) {}^{2} = 3118.5 \times \frac{7}{22} } \\ \\ \mathtt{ \: \: \Longrightarrow \: \: (r_2) {}^{2} = \frac{21829.5}{22} } \\ \\ \mathtt{ \: \: \Longrightarrow \: \: (r_2) {}^{2} =992.25 } \\ \\ \mathtt{ \: \: \Longrightarrow \: \: r_2 = \sqrt{992.25} } \\ \\ \mathtt{ \: \: \Longrightarrow \: \: r_2 =31.5 }$

$\mathtt{The \: radius \: \: of \: \: the \: \: second \: \: circle \: \: is \: \: 31.5 \: \: cm}</p><p></p><p>$

$\underline{ \mathfrak{ \: \: Now, \: \: }} \\ \\ \mathtt{The \: \: circumstances \: \: of \: \: the \: \: second \: \: } \\ \: \: \: \: \: \: \: \mathtt{circle =2\pi \: r_2} \\ \\ \: \: \: \: \: \: \: \mathtt{ = (2 \times \frac{22}{7} \times 31.5) \: cm} \\ \\ \: \: \: \: \: \: \: \mathtt{ = \frac{1386}{7} \: \: cm } \\ \\ \: \: \: \: \: \: \: \mathtt{ = 198 \: \: cm}$

$\: \: \: \: \text{The circumstance of the circle whose area} \\ \text{ is 36 \: times \: the area of circle with diameter} \\ \text{ 10.5 cm \: is \: \underline{ \: 198 \: cm} .}$