If the surface area of a cylinder with radius of 4 feet is 48pi square feet, what is its volume?
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
+26367 If the surface area of a cylinder with radius of 4 feet is 48pi square feet,
what is its volume?
\(\text{Let $V$ the volume of a cylinder.} \\ \text{Let $r$ the radius of a cylinder.} \\ \text{Let $h$ the height of a cylinder.} \\ \text{Let $S$ the surface area of a cylinder.}\)
\(\begin{array}{|lrcll|} \hline (1) & V &=& \pi r^2h \\ \\ \hline \\ & S &=& 2\pi r^2 + 2\pi rh \quad & | \quad -2\pi r^2 \\ (2) & S-2\pi r^2 &=& 2\pi rh \\ \\ \hline \\ \dfrac{(1)}{(2)} & \dfrac{V}{S-2\pi r^2} &=& \dfrac{\pi r^{2}h}{2\pi rh} \\\\ & \dfrac{V}{S-2\pi r^2} &=& \dfrac{\not{\pi} r^{\not{2}}\not{h}}{2\not{\pi} \not{r}\not{h}} \\\\ & \dfrac{V}{S-2\pi r^2} &=& \dfrac{r}{2} \quad & | \quad \cdot \left( S-2\pi r^2 \right) \\\\ & V &=& \dfrac{r}{2}\cdot \left(S-2\pi r^2 \right) \quad & | \quad S=48\pi,\quad r=4 \\\\ & V &=& \dfrac{4}{2}\cdot \left(48\pi-2\pi 4^2 \right) \\\\ & V &=& 2\cdot \left(48\pi-32\pi \right) \\\\ & V &=& 2\cdot \left(16\pi \right) \\\\ & \mathbf{V} &\mathbf{=}& \mathbf{32\pi \ feet^3 } \\ \hline \end{array}\)
