where is the epicenter of this hypothetical earthquake
Answers
Explanation:
Given:−
Radii of two circles = 48cm and 13cm
\underline{\sf \ \ \ \star\ To\ Find :- \ \ \ \ \ \ \ } ⋆ To Find:−
We have to find out the Area of that circle whose circumference is equal to the Difference of the circumference of given two circles
\underline{\sf \ \ \ \star\ Solution :- \ \ \ \ \ \ \ } ⋆ Solution:−
Find the Circumference of the two circles
\underline{\boxed{\sf{\dag\ \ Circumference\ of \ circle = 2 \pi r}}}† Circumference of circle=2πr
Find the circumference of circle whose radius is 48cm
\begin{gathered}\dashrightarrow\sf Circumference\ of \ Circle_1= 2\times \dfrac{22}{7}\times 48\\ \\ \\ \dashrightarrow\sf Circumference \ of \ Circle_1={\underline{\boxed{\purple{\sf \dfrac{2112}{7}}}}}\end{gathered}⇢Circumference of Circle1=2×722×48⇢Circumference of Circle1=72112
Find the circumference of circle whose radius is 13cm
\begin{gathered}\dashrightarrow\sf Circumference\ of \ Circle_2= 2\times \dfrac{22}{7}\times 13\\ \\ \\ \dashrightarrow\sf Circumference \ of \ Circle_2={\underline{\boxed{\red{\sf \dfrac{572}{7}}}}}\end{gathered}⇢Circumference of Circle2=2×722×13⇢Circumference of Circle2=7572
Now find out the circumference of new circle which is equal to the Difference of \sf C_1 - C_2C1−C2
\underline{\sf{\maltese \ Circumference\ of \ new \ circle= C_1- C_2}}✠ Circumference of new circle=C1−C2
\begin{gathered}:\implies\sf Circumference\ of \ new \ circle = \bigg[ \dfrac{2112}{7}\bigg]- \bigg[\dfrac{572}{7}\bigg]\\ \\ \\ :\implies\sf C.\ of \ new \ circle = \cancel{\dfrac{1540}{7}}\\ \\ \\ :\implies\sf C.\ of \ new \ circle = {\underline{\boxed{\purple{\sf 220cm}}}}\end{gathered}:⟹Circumference of new circle=[72112]−[7572]:⟹C. of new circle=71540:⟹C. of new circle=220cm
$$\rule{300}{1.5}$$
Now we have to find the Area of new circle
Find out the radius !
$$\begin{gathered}\dashrightarrow\sf Circumference\ of \ circle= 2 \pi r\\ \\ \\ \dashrightarrow\sf 220= 2\times \dfrac{22}{7}\times r \\ \\ \\\dashrightarrow\sf r= \dfrac{\cancel{220}\times 7}{\cancel{44}}\\ \\ \\ \dashrightarrow\sf r= 5\times 7\\ \\ \\\dashrightarrow{\underline{\boxed{\sf{\blue{ radius= 35cm}}}}}\end{gathered}$$
Now find the Area of new circle
$$\underline{\boxed{\sf{\ Area\ of \ circle= \pi r^2 }}}$$
$$\begin{gathered}\dashrightarrow\sf Area \ of \ circle= \dfrac{22}{\cancel{7}}\times \cancel{35}\times 35\\ \\ \\ \dashrightarrow\sf Area\ of \ circle = 22\times 5\times 35\\ \\ \\ \dashrightarrow\sf Area_{circle}= {\underline{\boxed{\sf{\purple{3850 cm^2}}}}}\end{gathered}$$
$$\underline{\underline{\textsf{ Area \ of \ new \ circle = {\textbf{3850sq.cm}}}}}$$
$$\rule{300}{1}$$
$$\underline{\sf{\bigstar\ Alternate\ Method \ To \ find \ Radius \ of \ new \ circle }}$$
$$\begin{gathered}\dashrightarrow\sf C_1- C_2= C_{new}\\ \\ \\ \dashrightarrow\sf 2\pi r_1-2\pi r_2= 2\pi r\\ \\ \\ \dashrightarrow\sf 2\pi(r_1-r_2)= 2\pi r\\ \\ \\ \dashrightarrow\sf \cancel{2 \pi}(48-13)= \cancel{2 \pi } r\ \ \ \ \Big[\therefore\ r_1=48\ ; \ r_2= 13 \Big]\\ \\ \\ \dashrightarrow{\boxed{\sf 35= r}}\end{gathered}$$
★By using this You can easily find the area of the new circle !
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The epicenter of a hypothethical earthqauake is located at the point where the earthquake starts to rupture. The point directly above the Earth's surface is the epicenter. It is the place where the strain energy is reserved in the rock is discharged which marks the point where the fault starts to explode.