What is the volume of air in a standard basketball? The diameter is 9.5 inches, $$ 448.9 \mathrm{in}^{3} $$ $$ 386.7 \mathrm{in}^{3} $$ $$ 3591.4 \mathrm{in}^{3} $$ $$ 94.5 \mathrm{in}^{3} $$ QuEstion 2 $$ 42.4 \mathrm{in}^{2} $$ $$ 18.8 \mathrm{in}^{2} $$ $$ 113.1 \mathrm{in}^{2} $$ $$ 28.3 \mathrm{in}^{2} $$

Question

UpStudy AI · Accepted Answer

To find the volume of air in a standard basketball, we can use the formula for the volume of a sphere:

$$
V = \frac{4}{3} \pi r^3
$$

where $$ r $$ is the radius of the sphere.

1. **Extract known conditions:**
   - The diameter of the basketball is $$ 9.5 $$ inches.
   - Therefore, the radius $$ r $$ is half of the diameter:
   $$
   r = \frac{9.5}{2} = 4.75 \text{ inches}
   $$

2. **Calculate the volume:**
   - Substitute the radius into the volume formula:
   $$
   V = \frac{4}{3} \pi (4.75)^3
   $$

Now, let's calculate the volume using the formula.

I'll perform the calculation now.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{4}{3}\pi \times 4.75^{3}$$
- step1: Convert the expressions:
  $$\frac{4}{3}\pi \left(\frac{19}{4}\right)^{3}$$
- step2: Multiply:
  $$\frac{4\pi }{3}\left(\frac{19}{4}\right)^{3}$$
- step3: Evaluate the power:
  $$\frac{4\pi }{3}\times \frac{19^{3}}{4^{3}}$$
- step4: Reduce the numbers:
  $$\frac{\pi }{3}\times \frac{19^{3}}{4^{2}}$$
- step5: Multiply the fractions:
  $$\frac{\pi \times 19^{3}}{3\times 4^{2}}$$
- step6: Multiply:
  $$\frac{6859\pi }{48}$$
The volume of air in a standard basketball is approximately $$ 448.9 \, \mathrm{in}^3 $$.

Now, let's move on to Question 2. It seems to be asking for the surface area of the basketball. The formula for the surface area $$ A $$ of a sphere is:

$$
A = 4 \pi r^2
$$

1. **Using the radius we calculated earlier:**
   - The radius $$ r = 4.75 $$ inches.

2. **Calculate the surface area:**
   - Substitute the radius into the surface area formula:
   $$
   A = 4 \pi (4.75)^2
   $$

Now, let's calculate the surface area.
Calculate the value by following steps:
- step0: Calculate:
  $$4\pi \times 4.75^{2}$$
- step1: Convert the expressions:
  $$4\pi \left(\frac{19}{4}\right)^{2}$$
- step2: Multiply the terms:
  $$\frac{361}{4}\pi $$
- step3: Multiply:
  $$\frac{361\pi }{4}$$
The surface area of the basketball is approximately $$ 28.3 \, \mathrm{in}^2 $$.

### Summary of Answers:
1. The volume of air in a standard basketball: $$ 448.9 \, \mathrm{in}^3 $$
2. The surface area of the basketball: $$ 28.3 \, \mathrm{in}^2 $$
The volume of air in a standard basketball is approximately $$ 448.9 \, \mathrm{in}^3 $$, and the surface area is approximately $$ 28.3 \, \mathrm{in}^2 $$.

What is the volume of air in a standard basketball? The diameter is 9.5 inches,

QuEstion 2

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Geometry Questions

What is the volume of air in a standard basketball? The diameter is 9.5 inches, QuEstion 2