Question

Find the area of the circle whose daimeter is :(Take π = 22/7)
1. 14 CM
2. 56 CM
3. 63 CM
4. 84 CM

​

Answer 1

$\huge\fbox\blue{GOOD~EVENING}$

$\huge\fbox\pink{Hope~it~helps}$

$\huge\fbox\blue{Refer~to~attachments}$

Answer 2

The areas of the four circles are 154 cm², 2464 cm², 3118.5 cm² and 5544 cm² respectively.

Step-by-step explanation:

${\underline{\underline{\bf{Given:}}}}$

• Diameter of circle₁ = 14 cm
• Diameter of circle₂ = 56 cm
• Diameter of circle₃ = 63 cm
• Diameter of circle₄ = 84 cm
• $\pi$ = $\sf{\frac{22}{7}}$

${\underline{\underline{\bf{To\: find:}}}}$

• The area of the four circles.

${\underline{\underline{\bf{Formula\:to\:be\: used:}}}}$

$\underline{\boxed{\sf{{Area}_{[Circle]}=\pi r^2\:sq.units}}}$

${\underline{\underline{\bf{Solution:}}}}$

We can find the areas of the circles by inserting the measure of radius in the formula:

$\leadsto{\sf{\purple{\pi r^2\:sq.units}}}$

But we are only given with the measures of diameter. So, first let's find the radius of the circles.

‎ ‎ ‎ ‎ ‎ ‎ ‎ ‎$\sf{ | | \: \dfrac{Diameter}{2} =Radius \: | | }$

$\begin{gathered}\boxed{\begin{array}{c|c}\sf Circle\:_{(1)}&\sf \dfrac{14}{2} = &\bf 7 \: cm \\ \\ \sf \: Circle\:_{(2)}& \sf \dfrac{56}{2} \: = & \bf 28 \: cm \\ \\ \sf \: Circle\:_{(3)}&\sf\dfrac{63}{2} = & \bf 31.5 \: cm\\ \\ \sf \: Circle\:_{(4)}& \sf \dfrac{84}{2} \: = & \bf 42 \: cm\end{array}}\end{gathered}$

Now, let's find the areas!

${\underline{\bf{Circle\:_{(1)}:}}}$

Radius = 7 cm

$\:$

$\:\:\:\:\:\:\:\::\implies{\sf{\dfrac{22}{7}\times 7^2}}$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\::\implies{\sf{\dfrac{22}{\cancel{7}}\times \cancel{7}\times 7}}$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\sf{22\times 7}}$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\underline{\underline{\frak{\red{154\:cm^2}}}}}$

$\:$

${\underline{\bf{Circle\:_{(2)}:}}}$

Radius = 28 cm

$\:$

$\:\:\:\:\:\:\:\::\implies{\sf{\dfrac{22}{7}\times 28^2}}$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\::\implies{\sf{\dfrac{22}{\cancel{7}}\times \cancel{28}\times 28}}$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\sf{22\times 4\times 28}}$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\underline{\underline{\frak{\red{2464\:cm^2}}}}}$

$\:$

${\underline{\bf{Circle\:_{(3)}:}}}$

Radius = 31.5 cm

$\:$

$\:\:\:\:\:\:\:\::\implies{\sf{\dfrac{22}{7}\times (31.5)^2}}$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\::\implies{\sf{\dfrac{22}{\cancel{7}}\times \cancel{31.5}\times 31.5}}$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\sf{22\times 4.5\times 31.5}}$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\underline{\underline{\frak{\red{3118.5\:cm^2}}}}}$

$\:$

${\underline{\bf{Circle\:_{(4)}:}}}$

Radius = 42 cm

$\:$

$\:\:\:\:\:\:\:\::\implies{\sf{\dfrac{22}{7}\times 42^2}}$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\::\implies{\sf{\dfrac{22}{\cancel{7}}\times \cancel{42}\times 42}}$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\sf{22\times 6\times 42}}$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\underline{\underline{\frak{\red{5544\:cm^2}}}}}$

__________________________________________