What's given in the question is the Circumference of the circle and what's asked is Area of the same. See there is no such direct formula to calculate the Area from Circumference (Although we can derive but it will be time consuming).
Circumference of Circle = 2πr (Circumference :a kind of Perimeter)
[tex] \bf \: Circumference \: of \: Circle = 2 \: \pi \: r[/tex]
Now 'π' has an approximate value 3.1415.. or simply 22/7. For easy calculation my suggestion is to use 22/7. Here I'm gonna use 3.1416 (correct upto 4 d.p.)
[tex] \sf \: r = \dfrac{176}{3.1416 \times 2} [/tex]
[tex] \sf \: r = 28.0112 \: cm \: (approx)[/tex]
Now,
[tex] \sf \: \: Area \: of \: Circle = \pi \: r²[/tex]
Now, since we have already calculated the value for 'r'
[tex] \bf \: Area \: of \: Circle = 3.1416 \times 28.0112 \times 28.0112[/tex]
Area of Circle = 2464.99 cm² (approx)
[Take this answer as a specimen (just an example) to solve the problem using the value for π equals to 3.1516 but still it's an advice to use 22/7 for easy calculation if it's not mentioned in the question]
Answers & Comments
Verified answer
Given:
To Find:
Solution:
Using Formula:
[tex]\\\large\bigstar \: { \underline{ \underline{ \boxed{ \bold{ \color{red}{circumference \: of \: circle = 2 \: \pi \: r}}}}} }\\\\[/tex]
by substituting values in the above formula;
[tex]\\\sf\implies circumference = \: 2 \: \pi \: r\\\\[/tex]
[tex]\sf\implies 176 = \: 2 \: \times \: \frac{22}{7} \: \times \: r \: \\\\[/tex]
[tex]\sf\implies 176 = \frac{44}{7} \: \times \: r \: \\\\[/tex]
[tex]\sf\implies r = \frac{ \cancel{176 }\times 7}{ \cancel{44}} \: \\\\ [/tex]
[tex]\sf\implies r =\frac{ 88\times 7} {22} \: \\\\ [/tex]
[tex]\sf\implies r = \frac{ \cancel{88}\times 7}{ \cancel{22}} \: \\\\[/tex]
[tex]\sf\implies r =4 \times 7 \: \\\\[/tex]
[tex]\implies{\bf{\pink{ r =28 \: cm\:}}} \\\\[/tex]
Calculating the Area of circle;
using formula:
[tex]\\\large\bigstar \: { \underline{ \underline{ \boxed{ \bold{ \color{pink}{Area \: of \: circle= \pi \: r²}}}}} }\\\\[/tex]
by substituting values in the above formula;
[tex]\\\sf\implies Area = \: \: \pi \: r²\\\\[/tex]
[tex]\sf\implies Area = \: \frac{22}{7} \: \times \: 28 \: \times \: 28\\\\[/tex]
[tex]\sf\implies Area = \: \frac{22}{\cancel{7}} \: \times \: \cancel{28 }\: \times \: 28\\\\[/tex]
[tex]\sf\implies Area = \: 22\: \times \: 4\: \times \: 28\\\\[/tex]
[tex]\sf\implies Area = \: 88\: \times \: 28\\\\[/tex]
[tex]\implies{\bf{\pink{ Area = 2464\: cm^2}}}\\\\[/tex]
hence, the area of circle is 2464 cm²
Heya !!
What's given in the question is the Circumference of the circle and what's asked is Area of the same. See there is no such direct formula to calculate the Area from Circumference (Although we can derive but it will be time consuming).
Circumference of Circle = 2πr (Circumference : a kind of Perimeter)
[tex] \bf \: Circumference \: of \: Circle = 2 \: \pi \: r[/tex]
Now 'π' has an approximate value 3.1415.. or simply 22/7. For easy calculation my suggestion is to use 22/7. Here I'm gonna use 3.1416 (correct upto 4 d.p.)
[tex] \sf \: 176 = 2 \times \: 3.1416 \: \times r[/tex]
[tex] \sf \: r = \dfrac{176}{3.1416 \times 2} [/tex]
[tex] \sf \: r = 28.0112 \: cm \: (approx)[/tex]
Now,
[tex] \sf \: \: Area \: of \: Circle = \pi \: r²[/tex]
Now, since we have already calculated the value for 'r'
[tex] \bf \: Area \: of \: Circle = 3.1416 \times 28.0112 \times 28.0112[/tex]
Area of Circle = 2464.99 cm² (approx)
[Take this answer as a specimen (just an example) to solve the problem using the value for π equals to 3.1516 but still it's an advice to use 22/7 for easy calculation if it's not mentioned in the question]