Question

find the surface area of a sphere with a circumference of 165 cm. Round to the nearest tenth.

A. 26.3 cm^2
B. 4333 cm^2
C. 8666 cm^2
D. 689.6 cm^2

Answer 1

If you know the circumference, C, the radius can be found from \[C = 2\pi r\]

Once you have the radius, the surface area of a sphere is given by \[A = 4\pi r^2\]

You can do this all in one equation if you solve for \(r\) in the first equation and substitute it into the second:

\[C = 2\pi r\]\[r = \frac{C}{2\pi}\]\[A = 4\pi r^2 = 4 \pi (\frac{C}{2\pi})^2 = \frac{4\pi C^2}{4\pi^2}=\frac{C^2}{\pi}\]

Answer 2

I'm lost.

Answer 3

When you get lost, do you typically ask for help, or just sit down and wait for starvation?

Do you understand the relationship between the circumference of a circle and its radius?\[C = 2\pi r\]We know \(C = 165 \text{ cm}\) and we know \(\pi\approx 3.14159\). Can you find \(r\)?