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A cylinder has a height of 17 inches and a diameter of 16 inches. What is its volume?
Use 3.14 and round your answer to the nearest hundredth.

cubic inches

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Answer:

The volume of cylinder is 3416.32 in³.

Step-by-step explanation:

Given :

  • [tex]\small\purple\bull[/tex] Diameter of cylinder = 16 in.
  • [tex]\small\purple\bull[/tex] Height of cylinder = 17 in.

[tex]\begin{gathered}\end{gathered}[/tex]

To Find :

  • [tex]\small\purple\bull[/tex] Radius of cylinder
  • [tex]\small\purple\bull[/tex] Volume of cylinder

[tex]\begin{gathered}\end{gathered}[/tex]

Using Formulas :

[tex]\star{\small{\underline{\boxed{\sf{\pink{R = \dfrac{D}{2}}}}}}}[/tex]

  • [tex]\blue\star[/tex] R = Radius
  • [tex]\blue\star[/tex] D = Diameter

[tex]\star{\small{\underline{\boxed{\sf{\pink{Volume_{(Cylinder)} =\pi{r}^{2}h}}}}}}[/tex]

  • [tex]\blue\star[/tex] π = 3.14
  • [tex]\blue\star[/tex] r = radius
  • [tex]\blue\star[/tex] h = height

[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]

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