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# Math

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If the surface area of a cylinder with radius of 4 feet is 48pi square feet, what is its volume?

Guest Aug 5, 2018
#1
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Volume = Pi x r^2 x h

S. Area  =[2 x pi x r x h] + [2 x pi x r^2]

48pi      =[2 x 3.141592 x 4 x h] + [2 x 3.141592 x 4^2], solve for h(height)

h            =2 feet

Volume =3.141592 x 4^2 x 2

=100.53 feet^3

Guest Aug 5, 2018
edited by Guest  Aug 5, 2018
#2
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If the surface area of a cylinder with radius of 4 feet is 48pi square feet,

what is its volume?

$$\text{Let V the volume of a cylinder.} \\ \text{Let r the radius of a cylinder.} \\ \text{Let h the height of a cylinder.} \\ \text{Let S the surface area of a cylinder.}$$

$$\begin{array}{|lrcll|} \hline (1) & V &=& \pi r^2h \\ \\ \hline \\ & S &=& 2\pi r^2 + 2\pi rh \quad & | \quad -2\pi r^2 \\ (2) & S-2\pi r^2 &=& 2\pi rh \\ \\ \hline \\ \dfrac{(1)}{(2)} & \dfrac{V}{S-2\pi r^2} &=& \dfrac{\pi r^{2}h}{2\pi rh} \\\\ & \dfrac{V}{S-2\pi r^2} &=& \dfrac{\not{\pi} r^{\not{2}}\not{h}}{2\not{\pi} \not{r}\not{h}} \\\\ & \dfrac{V}{S-2\pi r^2} &=& \dfrac{r}{2} \quad & | \quad \cdot \left( S-2\pi r^2 \right) \\\\ & V &=& \dfrac{r}{2}\cdot \left(S-2\pi r^2 \right) \quad & | \quad S=48\pi,\quad r=4 \\\\ & V &=& \dfrac{4}{2}\cdot \left(48\pi-2\pi 4^2 \right) \\\\ & V &=& 2\cdot \left(48\pi-32\pi \right) \\\\ & V &=& 2\cdot \left(16\pi \right) \\\\ & \mathbf{V} &\mathbf{=}& \mathbf{32\pi \ feet^3 } \\ \hline \end{array}$$

heureka  Aug 6, 2018