Globokim8

2021-02-26

A cylindrical can, open at the top, is to hold $470c{m}^{3}$ of liquid. Find the height and radius that minimize the amount of material needed to manufacture the can. Enter your answer with rational exponents, and use pi to represent pi.

Radius$=?$

Height$=?$

Radius

Height

coffentw

Skilled2021-02-27Added 103 answers

Given:

$V=470c{m}^{3}$

We have to find height and radius

$V=\pi {r}^{2}h=470$

$h-\frac{470}{\pi {r}^{2}}$

Plug this into the surface area equation

$SA=\pi {r}^{2}+2\pi rh$

$=\pi {r}^{2}+2\pi r(\frac{470}{\pi {r}^{2}})$

$=\pi {r}^{2}+\frac{940}{r}$

Differentiate SA and set to 0 solve for r

$\frac{dSA}{dr}=2\pi r-\frac{940}{{r}^{2}}=0$

$2\pi r=\frac{940}{{r}^{2}}$

${r}^{3}=\frac{940}{2}x$

${r}^{3}=\frac{470}{\pi}$

$r=(\frac{470}{\pi}{)}^{\frac{1}{3}}$

$=5.30cm$

Now, we find h:

$h=\frac{470}{\pi {r}^{2}}$

$=\frac{470}{\pi (5.30{)}^{2}}$

$=5.32cm$

We have to find height and radius

Plug this into the surface area equation

Differentiate SA and set to 0 solve for r

Now, we find h:

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

Which operation could we perform in order to find the number of milliseconds in a year??

$60\cdot 60\cdot 24\cdot 7\cdot 365$ $1000\cdot 60\cdot 60\cdot 24\cdot 365$ $24\cdot 60\cdot 100\cdot 7\cdot 52$ $1000\cdot 60\cdot 24\cdot 7\cdot 52?$ Tell about the meaning of Sxx and Sxy in simple linear regression,, especially the meaning of those formulas

Is the number 7356 divisible by 12? Also find the remainder.

A) No

B) 0

C) Yes

D) 6What is a positive integer?

Determine the value of k if the remainder is 3 given $({x}^{3}+k{x}^{2}+x+5)\xf7(x+2)$

Is $41$ a prime number?

What is the square root of $98$?

Is the sum of two prime numbers is always even?

149600000000 is equal to

A)$1.496\times {10}^{11}$

B)$1.496\times {10}^{10}$

C)$1.496\times {10}^{12}$

D)$1.496\times {10}^{8}$Find the value of$\mathrm{log}1$ to the base $3$ ?

What is the square root of 3 divided by 2 .

write $\sqrt[5]{{\left(7x\right)}^{4}}$ as an equivalent expression using a fractional exponent.

simplify $\sqrt{125n}$

What is the square root of $\frac{144}{169}$