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Answer :
To solve this problem, we need to find the volume of Cylinder B using the given information about the relationship between a cylinder's volume, its radius, and its height. The formula for the volume of a cylinder is:
[tex]\[ V = k \cdot r^2 \cdot h \][/tex]
where [tex]\( V \)[/tex] is the volume, [tex]\( r \)[/tex] is the radius, and [tex]\( h \)[/tex] is the height. [tex]\( k \)[/tex] is a constant of proportionality.
### Step 1: Find the value of [tex]\( k \)[/tex]
For Cylinder A:
- Volume [tex]\( V_A = 254.34 \)[/tex] cubic inches
- Radius [tex]\( r_A = 3 \)[/tex] inches
- Height [tex]\( h_A = 9 \)[/tex] inches
Substitute these values into the formula to find [tex]\( k \)[/tex]:
[tex]\[ 254.34 = k \cdot 3^2 \cdot 9 \][/tex]
[tex]\[ 254.34 = k \cdot 81 \][/tex]
Solve for [tex]\( k \)[/tex]:
[tex]\[ k = \frac{254.34}{81} \][/tex]
[tex]\[ k = 3.14 \][/tex]
### Step 2: Use the value of [tex]\( k \)[/tex] to find the volume of Cylinder B
For Cylinder B:
- Radius [tex]\( r_B = 4 \)[/tex] inches
- Height [tex]\( h_B = 5 \)[/tex] inches
Substitute these values and [tex]\( k = 3.14 \)[/tex] into the formula:
[tex]\[ V_B = 3.14 \cdot 4^2 \cdot 5 \][/tex]
[tex]\[ V_B = 3.14 \cdot 16 \cdot 5 \][/tex]
[tex]\[ V_B = 3.14 \cdot 80 \][/tex]
[tex]\[ V_B = 251.2 \][/tex]
Therefore, the volume of Cylinder B is 251.2 cubic inches. The correct answer is 251.2 cubic inches.
[tex]\[ V = k \cdot r^2 \cdot h \][/tex]
where [tex]\( V \)[/tex] is the volume, [tex]\( r \)[/tex] is the radius, and [tex]\( h \)[/tex] is the height. [tex]\( k \)[/tex] is a constant of proportionality.
### Step 1: Find the value of [tex]\( k \)[/tex]
For Cylinder A:
- Volume [tex]\( V_A = 254.34 \)[/tex] cubic inches
- Radius [tex]\( r_A = 3 \)[/tex] inches
- Height [tex]\( h_A = 9 \)[/tex] inches
Substitute these values into the formula to find [tex]\( k \)[/tex]:
[tex]\[ 254.34 = k \cdot 3^2 \cdot 9 \][/tex]
[tex]\[ 254.34 = k \cdot 81 \][/tex]
Solve for [tex]\( k \)[/tex]:
[tex]\[ k = \frac{254.34}{81} \][/tex]
[tex]\[ k = 3.14 \][/tex]
### Step 2: Use the value of [tex]\( k \)[/tex] to find the volume of Cylinder B
For Cylinder B:
- Radius [tex]\( r_B = 4 \)[/tex] inches
- Height [tex]\( h_B = 5 \)[/tex] inches
Substitute these values and [tex]\( k = 3.14 \)[/tex] into the formula:
[tex]\[ V_B = 3.14 \cdot 4^2 \cdot 5 \][/tex]
[tex]\[ V_B = 3.14 \cdot 16 \cdot 5 \][/tex]
[tex]\[ V_B = 3.14 \cdot 80 \][/tex]
[tex]\[ V_B = 251.2 \][/tex]
Therefore, the volume of Cylinder B is 251.2 cubic inches. The correct answer is 251.2 cubic inches.
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Rewritten by : Jeany
