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3 years ago

The height of a right cylinder is 3 times the radius of the base. The volume of the cylinder is 24pi cubic units.

Mathematics

1 answer:

bazaltina [42]3 years ago

3 0

Answer:

h = 6 units

Step-by-step explanation:

h = 3r

Volume = 24π

πr²h = 24π

πr² * 3r =24π

3πr³ =24π

r³ =24π / 3π

r³ = 8 = 2*2*2

r = 2 units

h = 3r = 3 *2 = 6 units

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Which graph represents the circle given by the equation x + y - 4x + 9y -7 = 0?

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<h3>How to determine the circle?</h3>

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Read 2 more answers

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$\begin{gathered} A=\frac{\theta}{360\degree}\times\pi r^2 \\ Where\text{ r}=AB=6\text{ units} \\ A=9\pi\text{ square units} \end{gathered}$

Substitute the values of the variables into the formula above to find the angle, θ, subtended by the sector.

$\begin{gathered} 9\pi=\frac{\theta}{360\degree}\times\pi\times6^2 \\ Crossmultiply \\ 9\pi\times360=36\pi\times\theta \\ 3240\pi=36\pi\theta \\ Divide\text{ both sides by 36}\pi \\ \frac{3240\pi}{36\pi}=\frac{36\pi\theta}{36\pi} \\ 90\degree=\theta \\ \theta=90\degree \end{gathered}$

To find the length of the arc, s, the formula is

$\begin{gathered} s=\frac{\theta}{360\degree}\times2\pi r \\ Where \\ \theta=90\degree \\ r=6\text{ units} \end{gathered}$

Substitute the variables into the formula to find the length of an arc, s above

$\begin{gathered} s=\frac{\theta}{360}\times2\pi r \\ s=\frac{90\degree}{360\degree}\times2\times\pi\times6 \\ s=\frac{12\pi}{4}=3\pi\text{ units} \\ s=3\pi\text{ units} \end{gathered}$

Hence, the length of the arc, s, is 3π units.

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Answer:

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Step-by-step explanation:

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