Please help me solve this!!

cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material for the sides of the can costs 0

Dafna11 [192]

Answer:

Radius=2.09 cm

Height,h=14.57 cm

Step-by-step explanation:

We are given that

Volume of cylinderical shaped can=200 cubic cm.

Cost of sides of can=0.02 cents per square cm

Cost of top and bottom of the can =0.07 cents per square cm

Curved surface area of cylinder= $2\pi rh$

Area of circular base=Area of circular top= $\pi r^2$

Total cost,C(r)= $0.02\times 2\pi rh+2\pi r^2\times 0.07$

Volume of cylinder, $V=\pi r^2 h$

$200=\pi r^2 h$

$h=\frac{200}{\pi r^2}$

Substitute the value of h

$C(r)=0.02\times 2\pi r\times \frac{200}{\pi r^2}+2\pi r^2\times 0.07$

$C(r)=\frac{8}{r}+0.14\pi r^2$

Differentiate w.r.t r

$C'(r)=-\frac{8}{r^2}+0.28\pi r$

$C'(r)=0$

$-\frac{8}{r^2}+0.28\pi r=0$

$0.28\pi r=\frac{8}{r^2}$

$r^3=\frac{8}{0.28\pi}=9.095$

$r=(9.095)^{\frac{1}{3}}=2.09$

Again, differentiate w.r.t r

$C''(r)=\frac{16}{r^3}+0.28\pi$

Substitute the value of r

$C''(2.09)=\frac{16}{(2.09)^3}+0.28\pi=2.63>0$

Therefore,the product cost is minimum at r=2.09

h= $\frac{200}{\pi (2.09)^2}=14.57$

Radius of can,r=2.09 cm

Height of cone,h=14.57 cm

4 0

3 years ago

The sum of a number and its square is 42. Which equation can be used to find the two numbers for which this is true?

tankabanditka [31]

Answer:

x² + x = 42

Step-by-step explanation:

Let the number be x then the square of this number is x²

Sum and equate to 42, that is

x² + x = 42

6 0

3 years ago

(x2 - y2)-(-x2 + y2)<br> How do you write that out to show work ?! Help pleAse

Verdich [7]

Answer:

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do it or he will hunt you down and kill u (lets destroy the moderators!!!!!!!!)

we are slowing them down already! good work soilders!

Step-by-step explanation:

8 0

2 years ago

Kate jogged a total distance of 8 1/2 miles during the months of January and February if katie only jogged 1/4 mile everyday whi

swat32

Since in this equation we are dividing 17/2 by 1/4, we can think of this as multiplying 17/2 with 4/1 (or 4).

17 4
---- X ----- = 34
2 1

Our final answer is 34 days.

3 0

3 years ago

What would you do if when you okay so he said yes would go?

Debora [2.8K]

I'm confused but no? lol

6 0

3 years ago