Question

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What is the diameter of a basketball with volume 270 cubic inches?

Use 3.14 for pi and round each answer to the nearest tenth.

Step 1: Substitute known values into the formula for volume
V = (4/3)pi r³ which is the same as V = 4 ÷ 3 ● pi r³

*blank 1* = 4 ÷ 3 ● *blank 2* ● *blank 3*

Options for blank 3

A r
B r³
C r²

Answer 1

To solve for the diameter of a basketball with a given volume, we start with the formula for the volume of a sphere:

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

Given that the volume \(V\) is 270 cubic inches, we can set up the equation:

\[
270 = \frac{4}{3} \cdot 3.14 \cdot r^3
\]

Next, we need to replace the values in the formula.

For **blank 1**, we have \(270\) as the volume:

\[
270 = \frac{4}{3} \cdot 3.14 \cdot *blank 2* \cdot *blank 3*
\]

In this case, **blank 2** corresponds to \(r\), and **blank 3** should be \(r^3\) because we need \(r\) cubed to calculate the volume.

Thus, the filled formula looks like this:

\[
270 = \frac{4}{3} \cdot 3.14 \cdot r \cdot r^3
\]

So the correct answers are:

- **blank 1**: 270
- **blank 2**: r
- **blank 3**: r³ (this is option B)

Now to summarize:

*blank 1* = 270
*blank 2* = r
*blank 3* = r³ (Option B)