1st of all we need to get everything into a consist system of units. For the volume V = 15 mL,
one mL = 1 cm 3 , so rather than try to convert this to cubic inches lets work with cm since the conversion from inches to cm is straight forward. 1 inch = 2.54 cm, so 4 inches x 2.54 cm per inch = 10.16 cm.
Now for a cylinder, volume = height (h) x area of the base (pi*radius squared).
so V = h*pi*r²
To find r we rearrange: r² = V/(h*pi) , so r = [V/(h*pi)]½
and d = 2*r
Solving for r we get r = [15 cm 3 /(10.16 cm * 3.14)] ½ = 0.69 cm
then d = 2*r =1.4 cm
Let's check our result. V = h*pi*r² , so V = 10.16 cm * pi * (0.69 cm)² = 15.2 cm³ ,
so we're right back where we started within round off errors.
Now if you like you can convert d = 1.4 cm back to inches : 1.4 cm / 2.54 cm per inch = 0.55 inches