To find the value of \( B \), the area of the base of the cylinder, we use the formula for the area of a circle, which is given by:
\[ B = \pi r^2 \]
where \( r \) is the radius of the base of the cylinder.
In this case, if the cylinder has a diameter of 10 inches, then the radius \( r \) would be:
\[ r = \frac{10}{2} = 5 \text{ inches} \]
To calculate the area of the base, plug the radius into the area formula:
\[ B = \pi (5)^2 = \pi (25) = 25\pi \]
However, based on the responses you've provided, it seems different measurements might be used. If the radius is specifically mentioned as 7 (for the option \(\pi(7)^2\)), that would use a radius of 7 inches:
\[ B = \pi(7)^2 = \pi(49) \]
Now going through the responses:
- π(10)²: This is the area of a circle with a radius of 10, which is incorrect.
- π(7)²: If the radius of the cylinder is 7 inches, this would correctly give us the base area.
- 2π(7): This expression does not represent the area of the base of a cylinder.
- 2π(10): This is also not the area of the base of the cylinder.
From the options provided and assuming we want to find \(B\) when \( r = 7\): The correct answer would be:
π(7)² (pi times 7 squared)