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The volume of this right circular cylinder is 64π cubic yards. If h, the height of the cylinder, is 4 yards, what is r, the radius of the base?

Sagot :

Answer:

4 yards

Step-by-step explanation:

The formula to determine the volume of the cylinder is the area of the circle (base of cylinder) multiplied by the height of the cylinder.

[tex]\rightarrow \pi r^{2} h = \text{Volume of cylinder}[/tex]

Substitute the height and the volume of the cylinder into the formula:

[tex]\rightarrow \pi r^{2} h = \text{Volume of cylinder}[/tex]

[tex]\rightarrow \pi (r^{2})( 4) = 64\pi[/tex]

Divide both sides by π and simplify:

[tex]\rightarrow \dfrac{\pi (r^{2})( 4)}{\pi } = \dfrac{64\pi}{\pi }[/tex]

[tex]\rightarrow { (r^{2})( 4)} = 64[/tex]

Divide both sides by 4 and simplify:
[tex]\rightarrow { \dfrac{(r^{2})( 4)}{4} } = \dfrac{64}{4}[/tex]

[tex]\rightarrow {{(r^{2}) = 16[/tex]

Take square root both sides and simplify:

[tex]\rightarrow \sqrt{r^{2}} = \sqrt{16}[/tex]

[tex]\rightarrow \sqrt{r \times r} = \sqrt{4 \times 4}[/tex]

[tex]\rightarrow r = 4 \ \text{yards}[/tex]

The radius of the base is 4 yards.
  • Height=h=4

[tex]\\ \rm\rightarrowtail V=\pi r^2h[/tex]

[tex]\\ \rm\rightarrowtail 64\pi=4\pi r^2[/tex]

[tex]\\ \rm\rightarrowtail 4r^2=64[/tex]

[tex]\\ \rm\rightarrowtail r^2=16[/tex]

[tex]\\ \rm\rightarrowtail r=4[/tex]

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