To find the area of the base of the cylinder using the formula provided, we will start by substituting \( r = 5 \) ft into the area of the base formula.
The area \( B \) of the base of the cylinder is given by:
\[ B = \pi r^2 \]
Substituting \( r = 5 \) ft:
\[ B = \pi (5)^2 \]
Calculating \( 5^2 \):
\[ 5^2 = 25 \]
Now, substitute back into the equation:
\[ B = \pi (25) = 25\pi \]
So, the area of the base of the cylinder is:
\[ B \approx 25 \cdot 3.14 \approx 78.5 , \text{ft}^2 \quad (\text{using } \pi \approx 3.14) \]
The volume \( V \) of the cylinder can be calculated using the volume formula:
\[ V = B \cdot h \]
Substituting \( B = 25\pi \) and \( h = 3 \) ft into the volume formula:
\[ V = 25\pi \cdot 3 = 75\pi \]
Thus, the volume of the cylinder is:
\[ V \approx 75 \cdot 3.14 \approx 235.5 , \text{ft}^3 \]
In summary:
- Area of the base \( B = 25\pi \approx 78.5 , \text{ft}^2 \)
- Volume \( V = 75\pi \approx 235.5 , \text{ft}^3 \)