What is the least common multiple of 4 and 6? * 1. 24 2. 12 3. 4 4. 6

The surface area of a right circular cone of radius r and height h is S = πr√ r 2 + h 2 , and its volume is V = 1 3 πr2h. What i

kirill115 [55]

Answer:

Required largest volume is 0.407114 unit.

Step-by-step explanation:

Given surface area of a right circular cone of radious r and height h is,

$S=\pi r\sqrt{r^2+h^2}$

and volume,

$V=\frac{1}{3}\pi r^2 h$

To find the largest volume if the surface area is S=8 (say), then applying Lagranges multipliers,

$f(r,h)=\frac{1}{3}\pi r^2 h$

subject to,

$g(r,h)=\pi r\sqrt{r^2+h^2}=8\hfill (1)$

We know for maximum volume $r\neq 0$ . So let $\lambda$ be the Lagranges multipliers be such that,

$f_r=\lambda g_r$

$\implies \frac{2}{3}\pi r h=\lambda (\pi \sqrt{r^2+h^2}+\frac{\pi r^2}{\sqrt{r^2+h^2}})$

$\implies \frac{2}{3}r h= \lambda (\sqrt{r^2+h^2}+\frac{ r^2}{\sqrt{r^2+h^2}})\hfill (2)$

And,

$f_h=\lambda g_h$

$\implies \frac{1}{3}\pi r^2=\lambda \frac{\pi rh}{\sqrt{r^2+h^2}}$

$\implies \lambda=\frac{r\sqrt{r^2+h^2}}{3h}\hfill (3)$

Substitute (3) in (2) we get,

$\frac{2}{3}rh=\frac{r\sqrt{R^2+h^2}}{3h}(\sqrt{R^2+h^2+}+\frac{r^2}{\sqrt{r^2+h^2}})$

$\implies \frac{2}{3}rh=\frac{r}{3h}(2r^2+h^2)$

$\implies h^2=2r^2$

Substitute this value in (1) we get,

$\pi r\sqrt{h^2+r^2}=8$

$\implies \pi r \sqrt{2r^2+r^2}=8$

$\implies r=\sqrt{\frac{8}{\pi\sqrt{3}}}\equiv 1.21252$

Then,

$h=\sqrt{2}(1.21252)\equiv 1.71476$

Hence largest volume,

$V=\frac{1}{3}\times \pi \times\frac{\pi}{8\sqrt{3}}\times 1.71476=0.407114$

3 0

3 years ago

Please Help!

MAVERICK [17]

For a translation of 4 units right, the graph will become -3(x-4). the 4 is negative to indicate that the translation is right.
For a vertical stretch of 4, the graph will become 4x-3(x-4)=-12(x-4).

With this information, g(x)=-12(x-4)

5 0

3 years ago

Quick anyone know this algebra 2 problem?

anastassius [24]

I believe it's the 3rd one

3 0

3 years ago

Albert made 48% of the shots he took during the basketball game if he made 12 shots how many shots did he attempt in total

Ymorist [56]

Wait sorry, I didn't read the question properly. The answer is 25 shots because 48% of those shots are in (Which is 12).

I hope you didn't get the question wrong because of me not reading the question properly. But this new answer, I hope it helps you. :)

5 0

2 years ago

Rosita went to the mall.She purchased a smoothie for $4,a scarf for $12,and a scrunchie for $8.Rosita plans to add 4+12+8 to det

enyata [817]

Answer:

4+12+8 = 24

Step-by-step explanation:

4+8=12 + 12 = 24 :)

5 0

3 years ago