Let's start with the formula for the volume of a sphere:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
Given that the volume [tex]\( V \)[/tex] is 435 cubic inches and using 3.14 for [tex]\(\pi\)[/tex], we need to find the radius [tex]\( r \)[/tex] of the sphere. We'll solve the equation step by step.
1. Substitute the given volume and the approximation for [tex]\(\pi\)[/tex] into the formula:
[tex]\[ 435 = \frac{4}{3} \times 3.14 \times r^3 \][/tex]
2. Isolate [tex]\( r^3 \)[/tex] by dividing both sides by [tex]\(\frac{4}{3} \times 3.14\)[/tex]:
[tex]\[ r^3 = \frac{435}{\frac{4}{3} \times 3.14} \][/tex]
3. Combine the constants on the right-hand side and simplify:
[tex]\[ r^3 = \frac{435 \times 3}{4 \times 3.14} \][/tex]
[tex]\[ r^3 = \frac{1305}{12.56} \][/tex]
[tex]\[ r^3 \approx 103.90127388535032 \][/tex]
4. To find [tex]\( r \)[/tex], take the cube root of both sides:
[tex]\[ r = \sqrt[3]{103.90127388535032} \][/tex]
[tex]\[ r \approx 4.701180839337921 \][/tex]
5. Round the radius to the nearest tenth of an inch:
[tex]\[ r \approx 4.7 \][/tex]
Thus, the radius of the basketball, rounded to the nearest tenth of an inch, is 4.7 inches. Therefore, the correct answer is:
[tex]\[ \boxed{4.7 \text{ inches}} \][/tex]
So, the answer is [tex]\( \text{D. 4.7 inches} \)[/tex].
