To find the surface area and volume of a sphere, you can use the following formulas:
- Surface Area (A): \[ A = 4\pi r^2 \]
- Volume (V): \[ V = \frac{4}{3}\pi r^3 \]
Here, \( r \) is the radius of the sphere. Since the diameter of the sphere is given as 86 inches, the radius \( r \) is half of the diameter:
\[ r = \frac{86}{2} = 43 \text{ inches} \]
Now, we'll calculate the surface area and volume using \( \pi \approx 3.14 \).
Surface Area Calculation
Using the surface area formula: \[ A = 4\pi r^2 \] Substituting \( r = 43 \): \[ A = 4 \times 3.14 \times (43)^2 \] Calculating \( (43)^2 \): \[ (43)^2 = 1849 \] Now plug that back into the surface area formula: \[ A = 4 \times 3.14 \times 1849 \approx 4 \times 3.14 \times 1849 \] Calculating: \[ 4 \times 3.14 = 12.56 \] Now multiply by 1849: \[ A \approx 12.56 \times 1849 \approx 23261.44 \text{ square inches} \]
Volume Calculation
Using the volume formula: \[ V = \frac{4}{3}\pi r^3 \] Substituting \( r = 43 \): \[ V = \frac{4}{3} \times 3.14 \times (43)^3 \] Calculating \( (43)^3 \): \[ (43)^3 = 79507 \] Now plug that back into the volume formula: \[ V \approx \frac{4}{3} \times 3.14 \times 79507 \] Calculating: \[ \frac{4}{3} \times 3.14 \approx 4.18667 \] Now multiply by 79507: \[ V \approx 4.18667 \times 79507 \approx 333098.415 \text{ cubic inches} \]
Final Answers
- The sphere's surface area is approximately 23261.44 square inches.
- The sphere's volume is approximately 333098.415 cubic inches.
Rounding these values, the surface area can be taken as 23261 square inches and the volume can be rounded to 333098 cubic inches.