A farm has two cylindrical silos for storing grain as shown. Silo A has a radius of 18 and a height of 20. Silo B has a radius of 12 and a height of 30. How much greater is the volume, in cubic feet, of the larger silo than the smaller silo? Use 3.14 for pi. Show your work. (3 points) Put responses in the correct input to answer the question.

Question

The volume of Silo A is Response area __ ft3.
The volume of Silo B is Response area__ ft3.
The volume of Silo A is ___ area cubic feet larger than the volume of the Silo B.

Answer 1

To find the volumes of the two silos, we will use the formula for the volume of a cylinder:

\[ V = \pi r^2 h \]

where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.

Volume of Silo A

• Radius (r) = 18 ft
• Height (h) = 20 ft

Calculating the volume of Silo A:

\[ V_A = \pi \times r^2 \times h = 3.14 \times (18)^2 \times 20 \]

First, calculate \( (18)^2 \):

\[ (18)^2 = 324 \]

Now plug it into the formula:

\[ V_A = 3.14 \times 324 \times 20 \]

Calculating \( 324 \times 20 \):

\[ 324 \times 20 = 6480 \]

Now calculate \( V_A \):

\[ V_A = 3.14 \times 6480 = 20365.2 , \text{ft}^3 \]

Volume of Silo B

• Radius (r) = 12 ft
• Height (h) = 30 ft

Calculating the volume of Silo B:

\[ V_B = \pi \times r^2 \times h = 3.14 \times (12)^2 \times 30 \]

First, calculate \( (12)^2 \):

\[ (12)^2 = 144 \]

Now plug it into the formula:

\[ V_B = 3.14 \times 144 \times 30 \]

Calculating \( 144 \times 30 \):

\[ 144 \times 30 = 4320 \]

Now calculate \( V_B \):

\[ V_B = 3.14 \times 4320 = 13579.2 , \text{ft}^3 \]

Difference in Volume

Now we find how much greater the volume of Silo A is compared to Silo B:

\[ \text{Difference} = V_A - V_B = 20365.2 - 13579.2 \]

Calculating the difference:

\[ 20365.2 - 13579.2 = 6786 \]

Final Responses

Now we fill in the response areas:

• The volume of Silo A is 20365.2 ft³.
• The volume of Silo B is 13579.2 ft³.
• The volume of Silo A is 6786 cubic feet larger than the volume of Silo B.