Answer:
b) Diameter = 6 inches and height 3 inches
Step-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 are
h= 3 in and h = 6 in
Volume V=28 c in
Part 1: When height h = 3 in
Formula 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 in
Hence Option B) is correct in first part. Let us see for the next part
Part 2:
V=28 c in , h= 6 in
Formula 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 inches
Hence none of the last two options are close to the answer.
Hence our final answer is b) Diameter = 6 inches and height 3 inches
