The formula for the volume of a sphere is [tex]$V=\frac{4}{3} \pi r^3$[/tex], where [tex]$V$[/tex] is the volume and [tex][tex]$r$[/tex][/tex] is the radius. Solve the formula for [tex]$r$[/tex], and then use it to answer the question.

The volume of a basketball is about 435 cubic inches.

What is the radius of the basketball, to the nearest tenth of an inch? Use 3.14 for [tex]$\pi$[/tex].

A. 4.3 inches
B. 4.5 inches
C. 4.1 inches
D. 4.7 inches



Answer :

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].