Question

find the surface area and volume of the sphere.
image of a sphere with a red dashed line labeled 11
round answer to 2 decimal places if needed.
surface area of sphere =
volume of sphere =
question help: read video maccana instructor

Explanation:

Step1: Identify the radius

The diameter of the sphere is given as 11, so the radius \( r=\frac{11}{2} = 5.5\).

Step2: Calculate Surface Area

The formula for the surface area of a sphere is \( SA = 4\pi r^{2}\).
Substitute \( r = 5.5\) into the formula:
\( SA=4\pi(5.5)^{2}=4\pi\times30.25 = 121\pi\approx121\times3.1416\approx380.13\)

Step3: Calculate Volume

The formula for the volume of a sphere is \( V=\frac{4}{3}\pi r^{3}\).
Substitute \( r = 5.5\) into the formula:
\( V=\frac{4}{3}\pi(5.5)^{3}=\frac{4}{3}\pi\times166.375=\frac{665.5}{3}\pi\approx\frac{665.5}{3}\times3.1416\approx706.86\)

Answer:

Surface Area of Sphere = \(\boldsymbol{380.13}\) (rounded to 2 decimal places)
Volume of Sphere = \(\boldsymbol{706.86}\) (rounded to 2 decimal places)