Answer:b) Diameter = 6 inches and height 3 inchesStep-by-step explanation:we are given the Volume of the cone as 28 and asked to determine the possible combination from the options. In these two options there are two different heights given . We will determine the radius or diameter for these two heights and thus can find the possible correct combination. The two heights areh= 3 in and h = 6 inVolume V=28 c inPart 1: When height h = 3 inFormula for Volume of a cone is give as [tex]V=\frac{1}{3} \pi r^2h[/tex]replacing the values [tex]\pi=3.14[/tex][tex]28=\frac{1}{3} \times 3.14 \times r^2 \times 3[/tex][tex]r^2=\frac{28}{3.14}[/tex][tex]r^2=8.909[/tex][tex]r=2.98[/tex]Diameter D = 2r = 5.96 ≈ 6 inHence Option B) is correct in first part. Let us see for the next partPart 2: V=28 c in , h= 6 inFormula for Volume of a cone is give as [tex]V=\frac{1}{3} \pi r^2h[/tex]replacing the values [tex]\pi=3.14[/tex][tex]28=\frac{1}{3} \times 3.14 \times r^2 \times 6[/tex][tex]r^2=\frac{28}{3.14 \times 2}[/tex][tex]r^2=4.45[/tex][tex]r=2.11[/tex]Diameter D = 2r = 4.22 inchesHence none of the last two options are close to the answer. Hence our final answer is b) Diameter = 6 inches and height 3 inches