Answer:
[tex] \displaystyle A _{ \text{vinyl record }} \approx 490 {cm}^{2} [/tex]
Step-by-step explanation:
we are given the circumstances of a vinyl record
we want to figure out the area
in order to do so we should figure out redious first
recall that,
[tex] \displaystyle \rm C = 2\pi r[/tex]
given that, C=78.5
thus substitute:
[tex] \displaystyle \rm 78.5= 2\pi r[/tex]
divide both sides by 2π:
[tex] \displaystyle r = \frac{78.5}{2\pi} [/tex]
we have figured out r now we'll figure out the area
remember that,
[tex] \displaystyle A _{ \text{circle}} = \pi {r}^{2} [/tex]
substitute the value of r
[tex] \displaystyle A _{ \text{vinyl record }} = \pi { \bigg(\frac{78 .5}{2\pi} \bigg)}^{2} [/tex]
by using calculator we acquire
[tex] \displaystyle A _{ \text{vinyl record }} = 490 {cm}^{2} [/tex]
