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.
Divide both sides by 3.14
The new equation is: 64.3 = r³
Cube root both sides
The new equation is: 8.0 = r
Step 4: Use the Answer with context to the problem.
If the radius of the basketball is *blank 1* inches, then the diameter is *blank 2* inches because the diameter is always twice as long as the radius.
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.
Divide both sides by 3.14
The new equation is: 64.3 = r³
Cube root both sides
The new equation is: 8.0 = r
Step 4: Use the Answer with context to the problem.
If the radius of the basketball is *blank 1* inches, then the diameter is *blank 2* inches because the diameter is always twice as long as the radius.
Answers
GPT-4o mini
Let's complete the calculations and fill in the blanks based on your steps.
1. **Step 1:** You have started with the formula for the volume of a sphere:
\[
V = \frac{4}{3} \pi r^3
\]
Substituting the volume (270 cubic inches) into the formula, we have:
\[
270 = \frac{4}{3} \cdot 3.14 \cdot r^3
\]
2. **Step 2:** Simplifying both sides gives:
\[
202.5 = 3.14 \cdot r^3
\]
3. **Step 3:** Now, solving for \(r^3\) by dividing both sides by 3.14:
\[
r^3 = \frac{202.5}{3.14} \approx 64.5
\]
(I made a correction here since you initially wrote \(64.3\), but you should be dividing \(202.5\) by \(3.14\)).
Now, let's find the cube root:
\[
r \approx \sqrt[3]{64.5} \approx 4.0 \text{ inches (rounded to the nearest tenth)}
\]
4. **Step 4:** Now, to find the diameter:
The diameter \(d\) is twice the radius:
\[
d = 2r \approx 2 \times 4.0 \approx 8.0 \text{ inches}
\]
Putting this all together:
If the radius of the basketball is **4.0** inches, then the diameter is **8.0** inches because the diameter is always twice as long as the radius.
So, the final answer to fill in the blanks is:
- **blank 1:** 4.0
- **blank 2:** 8.0
1. **Step 1:** You have started with the formula for the volume of a sphere:
\[
V = \frac{4}{3} \pi r^3
\]
Substituting the volume (270 cubic inches) into the formula, we have:
\[
270 = \frac{4}{3} \cdot 3.14 \cdot r^3
\]
2. **Step 2:** Simplifying both sides gives:
\[
202.5 = 3.14 \cdot r^3
\]
3. **Step 3:** Now, solving for \(r^3\) by dividing both sides by 3.14:
\[
r^3 = \frac{202.5}{3.14} \approx 64.5
\]
(I made a correction here since you initially wrote \(64.3\), but you should be dividing \(202.5\) by \(3.14\)).
Now, let's find the cube root:
\[
r \approx \sqrt[3]{64.5} \approx 4.0 \text{ inches (rounded to the nearest tenth)}
\]
4. **Step 4:** Now, to find the diameter:
The diameter \(d\) is twice the radius:
\[
d = 2r \approx 2 \times 4.0 \approx 8.0 \text{ inches}
\]
Putting this all together:
If the radius of the basketball is **4.0** inches, then the diameter is **8.0** inches because the diameter is always twice as long as the radius.
So, the final answer to fill in the blanks is:
- **blank 1:** 4.0
- **blank 2:** 8.0