Question

question 8
round answer to 2 decimal places if needed.
surface area of sphere =
volume of sphere =
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Explanation:

Step1: Recall formulas for sphere

The formula for the surface area of a sphere is \( SA = 4\pi r^{2} \), and the formula for the volume of a sphere is \( V=\frac{4}{3}\pi r^{3} \), where \( r \) is the radius of the sphere. Here, \( r = 6.4\space cm \).

Step2: Calculate Surface Area

Substitute \( r = 6.4 \) into the surface area formula:
\( SA=4\times\pi\times(6.4)^{2} \)
First, calculate \( (6.4)^{2}=40.96 \)
Then, \( 4\times\pi\times40.96 = 163.84\pi \)
Using \( \pi\approx3.14159 \), \( 163.84\times3.14159\approx514.72 \space cm^{2} \)

Step3: Calculate Volume

Substitute \( r = 6.4 \) into the volume formula:
\( V = \frac{4}{3}\times\pi\times(6.4)^{3} \)
First, calculate \( (6.4)^{3}=6.4\times6.4\times6.4 = 262.144 \)
Then, \( \frac{4}{3}\times\pi\times262.144=\frac{1048.576}{3}\pi \)
Using \( \pi\approx3.14159 \), \( \frac{1048.576}{3}\times3.14159\approx1097.50 \space cm^{3} \) (rounded to two decimal places)

Answer:

Surface Area of Sphere = \( \boldsymbol{514.72\space cm^{2}} \)
Volume of Sphere = \( \boldsymbol{1097.50\space cm^{3}} \)