Question

page 7 of 7 Volume of a Sphere Quick Check 2 of 52 of 5 Items Question Shakira is making a round piñata for a celebration. Her plan is to fill the inside with confetti. If the piñata measures 18 inches in diameter, what is its volume using 3.14 for pi and rounded to the nearest tenth?(1 point) Responses 24,416.7 inches3 24,416.7 inches cubed 3,052.1 inches3 3,052.1 inches cubed 339.1 inches3 339.1 inches cubed 113.0 inches3 113.0 inches cubed Skip to navigation

Answer 1

To calculate the volume of a sphere, you can use the formula:

\[
V = \frac{4}{3} \pi r^3
\]

Where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( \pi \) is approximately 3.14.

In your case, the diameter of the piñata is 18 inches. Therefore, the radius \( r \) is half of the diameter:

\[
r = \frac{18 \text{ inches}}{2} = 9 \text{ inches}
\]

Now, substitute the radius into the volume formula:

\[
V = \frac{4}{3} \times 3.14 \times (9)^3
\]

First, calculate \( 9^3 \):

\[
9^3 = 729
\]

Now, substitute that back into the formula:

\[
V = \frac{4}{3} \times 3.14 \times 729
\]

Calculating \( \frac{4}{3} \times 3.14 \):

\[
\frac{4}{3} \times 3.14 \approx 4.1867
\]

Now multiply that by 729:

\[
V \approx 4.1867 \times 729 \approx 3,055.6
\]

Rounding to the nearest tenth, the volume is approximately:

\[
V \approx 3,055.6 \text{ inches}^3
\]

Among the options provided, the closest answer is **3,052.1 inches cubed**. This suggests a slightly adjusted rounding, but it's the best match available.

So the correct response would be:

**3,052.1 inches cubed.**