Question

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What is the radius of a tennis ball with volume 150 cubic centimeters?

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

150 = 4 ÷ 3 ● 3.14 ● r³

Step 2: Simplify both sides of the equation.
150 = 4.18667 ● r³

Step 3: Solve the equation using inverse operations.

*blank 1* both sides by *blank 2*

The new equation is: *blank 3*

*blank 4* both sides
The new equation is: *blank 5* = *blank 6

Options for blank 1 and 4

A square root
B add
C multiply
D subtract
E cube root
F divide

Options for blank 3

A 145.8 = r³
B 35.7 = r³
C 47.8 = r³
D 115.4 = r³

Options for blank 6

A r³
B r
C 3²

Answers

GPT-4o mini
To find the radius of the tennis ball, we can follow the steps provided and fill in the blanks.

Starting with:

1. **Step 1**: We have the equation for volume \( V \):
\[ 150 = \frac{4}{3} \cdot 3.14 \cdot r^3 \]

2. **Step 2**: We simplify both sides:
\[ 150 = 4.18667 \cdot r^3 \]

3. **Step 3**: To isolate \( r^3 \), we need to divide both sides by \( 4.18667 \).

So, filling in the blanks:

- **Blank 1**: F (divide)
- **Blank 2**: 4.18667
- **Blank 3**: \( 35.7 = r^3 \) (after performing the calculation)
- **Blank 4**: E (cube root)
- **Blank 5**: \( r = \) (the new equation)
- **Blank 6**: A (r³)

So to summarize:

1. **Blank 1**: F (divide)
2. **Blank 2**: 4.18667
3. **Blank 3**: A (35.7 = r³)
4. **Blank 4**: E (cube root)
5. **Blank 5**: r =
6. **Blank 6**: A (r³)

Now we can find the radius \( r \) by calculating the cube root of 35.7:

Using a calculator or estimating cube roots:
- The cube root of 35.7 is approximately 3.3 (rounded to the nearest tenth).

Thus, the radius of the tennis ball is approximately **3.3 cm**.