To determine the height of 15 NBA basketballs stacked on top of each other, we first need to find the radius of a single basketball from the given surface area.
The formula for the surface area \( A \) of a sphere is:
\[ A = 4\pi r^2 \]
Given that the surface area of an official NBA basketball is \( 88.36\pi \):
\[ 4\pi r^2 = 88.36\pi \]
We can divide both sides by \( \pi \):
\[ 4r^2 = 88.36 \]
Next, divide both sides by 4:
\[ r^2 = \frac{88.36}{4} = 22.09 \]
Now take the square root of both sides to find the radius \( r \):
\[ r = \sqrt{22.09} \approx 4.69 \text{ inches} \]
The diameter \( d \) of the basketball is twice the radius:
\[ d = 2r \approx 2 \times 4.69 \approx 9.38 \text{ inches} \]
To find the total height of 15 basketballs stacked on top of each other, we multiply the diameter by 15:
\[ \text{Total height} = 15 \times d \approx 15 \times 9.38 \approx 140.7 \text{ inches} \]
Thus, the approximate height of 15 stacked NBA basketballs is:
\[ \boxed{140.7 \text{ inches}} \]