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
270 = 4 ÷ 3 ● r ● r³
Step 2: Simplify both sides of the equation.
202.5 = 3.14 ● 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 divide
B add
C subtract
D multiply
E cube root
F square root
Options for blank 3
A 202.5 = r ^ 3
B 64.3 = r ^ 3
C 64.3 = r ^ 2
D 64.3 = r
E 202.5 = r ^ 2
F 202.5 = r
Options for blank 6
A r²
B r
C r³
Make sure all blanks are correct
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
270 = 4 ÷ 3 ● r ● r³
Step 2: Simplify both sides of the equation.
202.5 = 3.14 ● 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 divide
B add
C subtract
D multiply
E cube root
F square root
Options for blank 3
A 202.5 = r ^ 3
B 64.3 = r ^ 3
C 64.3 = r ^ 2
D 64.3 = r
E 202.5 = r ^ 2
F 202.5 = r
Options for blank 6
A r²
B r
C r³
Make sure all blanks are correct
Answers
GPT-4o mini
To solve for the diameter of a basketball with a volume of 270 cubic inches using the formula for the volume of a sphere, let's follow the steps you've outlined.
### Step 1: Substitute known values into the formula for volume
The formula for the volume \( V \) of a sphere is given by:
\[
V = \frac{4}{3} \pi r^3
\]
Substituting \( V = 270 \) and \( \pi = 3.14 \):
\[
270 = \frac{4}{3} \cdot 3.14 \cdot r^3
\]
### Step 2: Simplify both sides of the equation.
First, calculate \( \frac{4}{3} \cdot 3.14 \):
\[
\frac{4}{3} \cdot 3.14 \approx 4.1867 \text{ (approximately)}
\]
Then we can rewrite the equation as:
\[
270 = 4.1867 \cdot r^3
\]
Now, let's simplify this further. To make it simpler, we will first multiply by \( \frac{3}{4} \):
\[
202.5 = 3.14 \cdot r^3
\]
### Step 3: Solve the equation using inverse operations.
1. **For blank 1**, we will "divide."
**For blank 2**, we divide by 3.14.
**For blank 3**, the new equation is \( 64.3 = r^3 \).
So:
**Blank 1**: A (divide)
**Blank 2**: 3.14
**Blank 3**: B (64.3 = r³)
2. Now, we need to take the cube root of both sides to solve for \( r \).
**For blank 4**, we will "take the cube root."
**For blank 5**, we write that \( r = \)
**For blank 6**, we have \( 64.3^{1/3} \).
So:
**Blank 4**: E (cube root)
**Blank 5**: r
**Blank 6**: B (r)
Now we will calculate \( r \):
Using a calculator, \( r = \sqrt[3]{64.3} \approx 4.0 \) (rounded to the nearest tenth).
### Final Calculation for Diameter
The diameter \( d \) is twice the radius \( r \):
\[
d = 2r = 2 \cdot 4.0 = 8.0 \text{ inches}
\]
### Summary of Blanks
1. **Blank 1**: A (divide)
2. **Blank 2**: 3.14
3. **Blank 3**: B (64.3 = r³)
4. **Blank 4**: E (cube root)
5. **Blank 5**: r
6. **Blank 6**: B (r)
The diameter of the basketball is approximately \( 8.0 \) inches.
### Step 1: Substitute known values into the formula for volume
The formula for the volume \( V \) of a sphere is given by:
\[
V = \frac{4}{3} \pi r^3
\]
Substituting \( V = 270 \) and \( \pi = 3.14 \):
\[
270 = \frac{4}{3} \cdot 3.14 \cdot r^3
\]
### Step 2: Simplify both sides of the equation.
First, calculate \( \frac{4}{3} \cdot 3.14 \):
\[
\frac{4}{3} \cdot 3.14 \approx 4.1867 \text{ (approximately)}
\]
Then we can rewrite the equation as:
\[
270 = 4.1867 \cdot r^3
\]
Now, let's simplify this further. To make it simpler, we will first multiply by \( \frac{3}{4} \):
\[
202.5 = 3.14 \cdot r^3
\]
### Step 3: Solve the equation using inverse operations.
1. **For blank 1**, we will "divide."
**For blank 2**, we divide by 3.14.
**For blank 3**, the new equation is \( 64.3 = r^3 \).
So:
**Blank 1**: A (divide)
**Blank 2**: 3.14
**Blank 3**: B (64.3 = r³)
2. Now, we need to take the cube root of both sides to solve for \( r \).
**For blank 4**, we will "take the cube root."
**For blank 5**, we write that \( r = \)
**For blank 6**, we have \( 64.3^{1/3} \).
So:
**Blank 4**: E (cube root)
**Blank 5**: r
**Blank 6**: B (r)
Now we will calculate \( r \):
Using a calculator, \( r = \sqrt[3]{64.3} \approx 4.0 \) (rounded to the nearest tenth).
### Final Calculation for Diameter
The diameter \( d \) is twice the radius \( r \):
\[
d = 2r = 2 \cdot 4.0 = 8.0 \text{ inches}
\]
### Summary of Blanks
1. **Blank 1**: A (divide)
2. **Blank 2**: 3.14
3. **Blank 3**: B (64.3 = r³)
4. **Blank 4**: E (cube root)
5. **Blank 5**: r
6. **Blank 6**: B (r)
The diameter of the basketball is approximately \( 8.0 \) inches.