Answer:(D) 30pi inchesStep-by-step explanation:First, we use the given volume, the given height, and the formula of the volume of a cylinder to find the radius of the base. Then we use the radius of the base to find the circumference of the base.[tex] volume = \pi r^2 h [/tex][tex] volume = 6750 \pi~in.^3 [/tex]We set the formula equal to the volume and replace h with 30 in.[tex] \pi r^2 h = 6750 \pi~in.^3 [/tex][tex] \pi r^2 \times 30 ~in. = 6750 \pi~in.^3 [/tex]Divide both sides by 30pi in.[tex] r^2 = 225 ~in.^2 [/tex]Take the square root of each side.[tex] \sqrt{r^2} = \sqrt{225 ~in.^2} [/tex][tex] r = 15~in. [/tex]The radius of the base is 15 in.Now we use the radius of the base and the formula of the circumference of a circle to find the answer.[tex] circumference = 2 \pi r [/tex][tex] circumference = 2 \pi \times 15~in. [/tex][tex] circumference = 30 \pi ~in. [/tex]