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
*blank 1* = 4 ÷ 3 ● *blank 2* ● *blank 3*
Options for blank 3
A r²
B r
C r³
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
*blank 1* = 4 ÷ 3 ● *blank 2* ● *blank 3*
Options for blank 3
A r²
B r
C r³
Answers
GPT-4o mini
To find the radius of a tennis ball with a volume of 150 cubic centimeters, we will use the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
In your instruction, you want to substitute the known values into the formula for volume. Given that:
- V = 150 cm³
- We will use \( \pi = 3.14 \)
So, we can substitute these values into the formula:
\[ 150 = \frac{4}{3} \cdot 3.14 \cdot r^3 \]
Now, filling in the blanks:
*blank 1* represents the volume \( V \) (which is 150), and we would replace it in the equation later.
*blank 2* represents \( \pi \) (which is 3.14).
*blank 3* should represent \( r^3 \) since it's the term we are solving for.
Thus, you would fill in:
- *blank 1*: 150
- *blank 2*: 3.14
- *blank 3*: C (which is \( r^3 \))
So the complete substitution looks like this:
150 = \( \frac{4}{3} \cdot 3.14 \cdot r^3 \)
Now, to solve for \( r \):
1. Multiply both sides by \( \frac{3}{4} \) to isolate \( r^3 \):
\[ r^3 = \frac{150 \cdot 3}{4 \cdot 3.14} \]
2. Now calculate \( r^3 \):
\[ r^3 = \frac{450}{12.56} \approx 35.8 \]
3. Now take the cube root to find \( r \):
\[ r \approx \sqrt[3]{35.8} \approx 3.3 \text{ cm} \]
So the radius of the tennis ball is approximately **3.3 cm** when rounded to the nearest tenth.
\[ V = \frac{4}{3} \pi r^3 \]
In your instruction, you want to substitute the known values into the formula for volume. Given that:
- V = 150 cm³
- We will use \( \pi = 3.14 \)
So, we can substitute these values into the formula:
\[ 150 = \frac{4}{3} \cdot 3.14 \cdot r^3 \]
Now, filling in the blanks:
*blank 1* represents the volume \( V \) (which is 150), and we would replace it in the equation later.
*blank 2* represents \( \pi \) (which is 3.14).
*blank 3* should represent \( r^3 \) since it's the term we are solving for.
Thus, you would fill in:
- *blank 1*: 150
- *blank 2*: 3.14
- *blank 3*: C (which is \( r^3 \))
So the complete substitution looks like this:
150 = \( \frac{4}{3} \cdot 3.14 \cdot r^3 \)
Now, to solve for \( r \):
1. Multiply both sides by \( \frac{3}{4} \) to isolate \( r^3 \):
\[ r^3 = \frac{150 \cdot 3}{4 \cdot 3.14} \]
2. Now calculate \( r^3 \):
\[ r^3 = \frac{450}{12.56} \approx 35.8 \]
3. Now take the cube root to find \( r \):
\[ r \approx \sqrt[3]{35.8} \approx 3.3 \text{ cm} \]
So the radius of the tennis ball is approximately **3.3 cm** when rounded to the nearest tenth.