Question

what is the surface area of a sphere with a circumference of 30 ft im lost and i need directions not just a answer

Answer 1

SA=4pir^2
c=2pir
so
c=30
30=2pir
divide 2
15=pir
divide by pi
15/pi=r
sub

SA=4pir^2
SA=4pi(15/pi)^2
SA=4pi(225/pi^2)
SA=900/pi squaer feet
if use pi=3.141592
SA=286.47889756541160438399077407053 square feet or about 286 square feet

Answer 2

Circumference(C) and surface area(S) of the sphere is given by:

`C = 2 \pi r`

`S = 4 \pi r^2`

where, r is the radius of the sphere.

As per the statement:

Circumference(C) = 30 ft

then;

`30 = 2 \pi r`

Divide both sides by
`2 \pi` we have;

`(15)/(\pi) =r`

or

`r=(15)/(\pi)` ft

We have to find the Surface area of sphere.

Substitute the given values we have;

`S = 4 \pi \cdot ((15)/(\pi))^2`

⇒
`S = 4 \pi \cdot (225)/((\pi)^2)`

⇒
`S = 4 \cdot (225)/(\pi)`

Use
`\pi=3.14`

then;

`S = 4 \cdot (225)/(3.14)`

Simplify:

S = 286.624204 square feet

Therefore, the surface area of a sphere is, 286.624204 square feet