To find the difference in volume between the two cylindrical silos, we will use the formula for the volume \( V \) of a cylinder:
\[ V = \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height of the cylinder.
Step 1: Calculate the Volume of Silo A
For Silo A:
- Height \( h_A = 20 \) ft
- Radius \( r_A = 18 \) ft
Substituting these values into the volume formula:
\[ V_A = \pi r_A^2 h_A = 3.14 \times (18^2) \times 20 \]
Calculating \( 18^2 \):
\[ 18^2 = 324 \]
Now substitute \( 324 \) back into the volume formula:
\[ V_A = 3.14 \times 324 \times 20 \]
Calculating \( 324 \times 20 \):
\[ 324 \times 20 = 6480 \]
Now calculate the volume for Silo A:
\[ V_A = 3.14 \times 6480 \]
Calculating \( 3.14 \times 6480 \):
\[ V_A = 20357.2 \text{ cubic feet} \]
Step 2: Calculate the Volume of Silo B
For Silo B:
- Height \( h_B = 30 \) ft
- Radius \( r_B = 12 \) ft
Substituting these values into the volume formula:
\[ V_B = \pi r_B^2 h_B = 3.14 \times (12^2) \times 30 \]
Calculating \( 12^2 \):
\[ 12^2 = 144 \]
Now substitute \( 144 \) back into the volume formula:
\[ V_B = 3.14 \times 144 \times 30 \]
Calculating \( 144 \times 30 \):
\[ 144 \times 30 = 4320 \]
Now calculate the volume for Silo B:
\[ V_B = 3.14 \times 4320 \]
Calculating \( 3.14 \times 4320 \):
\[ V_B = 13596.8 \text{ cubic feet} \]
Step 3: Find the Difference in Volume
Now, we find the difference between the two volumes:
\[ \text{Difference} = V_A - V_B \]
Substituting the values we calculated:
\[ \text{Difference} = 20357.2 - 13596.8 \]
Calculating the difference:
\[ \text{Difference} = 6750.4 \text{ cubic feet} \]
Final Answer
The volume of the larger silo is 6750.4 cubic feet greater than the volume of the smaller silo.
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