Sure! Let's solve the problem step-by-step.
We are given that the area of the base of the cylindrical tank is 154 square feet. We need to find the radius and the circumference of the base.
First, let's recall the formula for the area of a circle:
[tex]\[ \text{Area} = \pi r^2 \][/tex]
Where [tex]\( r \)[/tex] is the radius of the base.
We are told to use [tex]\( \pi = \frac{22}{7} \)[/tex]. Given the area of the base is 154 square feet, we can set up the equation:
[tex]\[ 154 = \frac{22}{7} r^2 \][/tex]
To solve for [tex]\( r \)[/tex], follow these steps:
1. Multiply both sides of the equation by 7 to eliminate the fraction on the right side:
[tex]\[ 154 \times 7 = 22 r^2 \][/tex]
[tex]\[ 1078 = 22 r^2 \][/tex]
2. Divide both sides by 22 to isolate [tex]\( r^2 \)[/tex]:
[tex]\[ \frac{1078}{22} = r^2 \][/tex]
[tex]\[ 49 = r^2 \][/tex]
3. Take the square root of both sides to solve for [tex]\( r \)[/tex]:
[tex]\[ r = \sqrt{49} \][/tex]
[tex]\[ r = 7 \][/tex]
The radius of the base is 7 feet.
Next, we need to find the circumference of the base. The formula for the circumference of a circle is:
[tex]\[ \text{Circumference} = 2 \pi r \][/tex]
Using [tex]\( \pi = \frac{22}{7} \)[/tex] and [tex]\( r = 7 \)[/tex]:
[tex]\[ \text{Circumference} = 2 \times \frac{22}{7} \times 7 \][/tex]
Now, simplify the expression:
[tex]\[ \text{Circumference} = 2 \times 22 \][/tex]
[tex]\[ \text{Circumference} = 44 \][/tex]
So, the circumference of the base is 44 feet.
Therefore, the radius of the base of the cylindrical tank is 7 feet, and the circumference is 44 feet.
