To find the surface area and volume of a sphere, you can use the following formulas:
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Surface Area (SA): \[ SA = 4\pi r^2 \]
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Volume (V): \[ V = \frac{4}{3}\pi r^3 \]
Given that the radius \( r \) of the sphere is 63 inches and using \( \pi \approx 3.14 \):
Step 1: Calculate the Surface Area
\[ SA = 4 \cdot 3.14 \cdot (63)^2 \] First, calculate \( 63^2 \): \[ 63^2 = 3969 \] Then, calculate the surface area: \[ SA = 4 \cdot 3.14 \cdot 3969 = 12.56 \cdot 3969 \] Now calculating \( 12.56 \cdot 3969 \): \[ SA \approx 49815.84 \]
Step 2: Calculate the Volume
\[ V = \frac{4}{3} \cdot 3.14 \cdot (63)^3 \] First, calculate \( 63^3 \): \[ 63^3 = 63 \cdot 3969 = 250047 \] Now, calculate the volume: \[ V = \frac{4}{3} \cdot 3.14 \cdot 250047 \] Calculating \( \frac{4}{3} \cdot 3.14 = 4.186667 \) approximately. Now, \[ V \approx 4.186667 \cdot 250047 \approx 1041866.25 \]
Final Results
- The surface area of the sphere is approximately 49815.84 square inches.
- The volume of the sphere is approximately 1041866.25 cubic inches.