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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 :

4030859

Answer:

h = 4 cm

Step-by-step explanation:

The formula for volume of a cylinder is

V = πr²h      where V is the volume, r is the radius, and h is the height.

We are given V = 64π, and r = 4, plug those in and solve for h

64π = π(4²)h

64π = 16πh

(64π)/(16π) = (16πh)/(16π)      (divide both sides by 16π)

4 = (16π)/(16π)h

 4 = h

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Answer:

  • Radius = 4 yards

Solution:

Here, we are provided a right circular cylinder with :

  • Volume = 64 π cubic yards
  • Height = 4 yards
  • Radius = ?

We know that :

[tex] \quad\hookrightarrow\quad{\pmb{ \mathfrak { Volume = \pi r^2 h }}}[/tex]

Therefore,

[tex] \implies\quad \sf{V = \pi r^2 h }[/tex]

[tex] \implies\quad \sf{64\pi = \pi r^2 \times 4 }[/tex]

[tex] \implies\quad \sf{ \pi r^2 \times 4 = 64\pi}[/tex]

[tex] \implies\quad \sf{r^2 =\dfrac{64\pi}{\pi \times 4} }[/tex]

[tex] \implies\quad \sf{ r^2 =\dfrac{\cancel{64}}{\cancel{4}}\times \cancel{\dfrac{\pi}{\pi}}}[/tex]

[tex] \implies\quad \sf{ r^2 = 16}[/tex]

[tex] \implies\quad \sf{r=\sqrt{16} }[/tex]

[tex] \implies\quad \underline{\underline{\pmb{\sf{r= 4}}} }[/tex]

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