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
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**.
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**.