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Answer:
The volume of cylinder is 3416.32 in³.
Step-by-step explanation:
Given :
[tex]\begin{gathered}\end{gathered}[/tex]
To Find :
[tex]\begin{gathered}\end{gathered}[/tex]
Using Formulas :
[tex]\star{\small{\underline{\boxed{\sf{\pink{R = \dfrac{D}{2}}}}}}}[/tex]
[tex]\star{\small{\underline{\boxed{\sf{\pink{Volume_{(Cylinder)} =\pi{r}^{2}h}}}}}}[/tex]
[tex]\begin{gathered}\end{gathered}[/tex]
Solution :
Here we have given that the diameter of cylinder is 16 in. So, finding the radius of cylinder by substituting the values in the formula :
[tex]{\longmapsto{\sf{Radius_{(Cylinder)} = \dfrac{D}{2}}}}[/tex]
[tex]{\longmapsto{\sf{Radius_{(Cylinder)} = \dfrac{16}{2}}}}[/tex]
[tex]{\longmapsto{\sf{Radius_{(Cylinder)} = \cancel{\dfrac{16}{2}}}}}[/tex]
[tex]{\longmapsto{\sf{Radius_{(Cylinder)} = 8 \: in}}}[/tex]
[tex]\star\underline{\boxed{\sf{\red{Radius_{(Cylinder)} = 8 \: in}}}}[/tex]
Hence, the radius of cylinder is 8 in.
[tex]\begin{gathered}\end{gathered}[/tex]
Now, finding the volume of cylinder by substituting the values in the formula :
[tex]{\longrightarrow{\sf{Volume_{(Cylinder)} =\pi{r}^{2}h}}}[/tex]
[tex]{\longrightarrow{\sf{Volume_{(Cylinder)} =3.14 \times {(8)}^{2} \times 17}}}[/tex]
[tex]{\longrightarrow{\sf{Volume_{(Cylinder)} =3.14 \times {(8 \times 8)}\times 17}}}[/tex]
[tex]{\longrightarrow{\sf{Volume_{(Cylinder)} =3.14 \times {(64)}\times 17}}}[/tex]
[tex]{\longrightarrow{\sf{Volume_{(Cylinder)} =3.14 \times 64\times 17}}}[/tex]
[tex]{\longrightarrow{\sf{Volume_{(Cylinder)} =200.96\times 17}}}[/tex]
[tex]{\longrightarrow{\sf{Volume_{(Cylinder)} =3416.32 \: {in}^{3}}}}[/tex]
[tex]\star{\underline{\boxed{\sf{\red{Volume_{(Cylinder)} =3416.32 \: {in}^{3}}}}}}[/tex]
Therefore, the volume of cylinder is 3416.32 in³.
[tex]\rule{300}{2.5}[/tex]