menu
bartleby
search
close search
Hit Return to see all results

ProductRadius (inches)Height (inches)Volume (cubic inches)Baking power1.253.6517.92Cleanser1.457.5049.54Coffee1.955.2062.12Frosting1.633.6030.05Pineapple juice2.106.7092.82Using the given information above complete the table below.**I just need to get the ball rolling I got the first one. I need Coffee, Frosting, and Pineapple Juice. ProductActualVolumeActual RadiusActual Surface AreaRadius ofMinimized areaHeight ofMinimized areaMinimized Surface AreaBaking powder17.921.25    Cleanser49.541.45    Coffee62.121.95    Frosting30.051.63    Pineapple juice92.822.10

Question

 

Product

Radius (inches)

Height (inches)

Volume (cubic inches)

Baking power

1.25

3.65

17.92

Cleanser

1.45

7.50

49.54

Coffee

1.95

5.20

62.12

Frosting

1.63

3.60

30.05

Pineapple juice

2.10

6.70

92.82

Using the given information above complete the table below.

**I just need to get the ball rolling I got the first one. I need Coffee, Frosting, and Pineapple Juice.

 

Product

Actual

Volume

Actual Radius

Actual Surface Area

Radius of

Minimized area

Height of

Minimized area

Minimized Surface Area

Baking powder

17.92

1.25

       

Cleanser



49.54

1.45

       

Coffee



62.12

1.95

       

Frosting



30.05

1.63

       

Pineapple juice

92.82

2.10

       
check_circleAnswer
Step 1

Assuming all the items are in cylindrical shape. Look for the coffee can: The volume V is 62.12 in3; consider the radius r, and height h. Then, obtain the value of h in terms of r.

V = ar?h
62.12 rh
62.12
h=
лr?
Obtain the surface area in terms ofr as follows
A 27rh2r
62.12
+2r
nr2
A 2Tr
124.242r
A(r)
+
r
Observe that the radius can neither be zero nornegative, hence the domain is (0,0).
Z
help_outline

Image Transcriptionclose

V = ar?h 62.12 rh 62.12 h= лr? Obtain the surface area in terms ofr as follows A 27rh2r 62.12 +2r nr2 A 2Tr 124.242r A(r) + r Observe that the radius can neither be zero nornegative, hence the domain is (0,0). Z

fullscreen
Step 2

The derivative of function of surface area becomes

124.24
-+4Tr 4nr -124.24
A'(r)
r
Analyze the sign: As the square ofr is always positive, then only need is to find the sign
of numerator whether it is positive or negative. Equate the numerator to zero and obtain r.
4Tr3-124.4= 0
31.062.15
r3
Around the above value ofr, the sign of derivative is different. Ifthe radius is less than
2.15 in, the surface area is decreasing as the derivative is negative. Ifthe radius is more
than 2.15 in, the surface area is increasing as the derivative is positive. The height|
62.12
becomes h
4.3 in, and the minimize surface area becomes
31.06
124.242(2.15) -
A(r)=
(2.15)
86.83 in2
help_outline

Image Transcriptionclose

124.24 -+4Tr 4nr -124.24 A'(r) r Analyze the sign: As the square ofr is always positive, then only need is to find the sign of numerator whether it is positive or negative. Equate the numerator to zero and obtain r. 4Tr3-124.4= 0 31.062.15 r3 Around the above value ofr, the sign of derivative is different. Ifthe radius is less than 2.15 in, the surface area is decreasing as the derivative is negative. Ifthe radius is more than 2.15 in, the surface area is increasing as the derivative is positive. The height| 62.12 becomes h 4.3 in, and the minimize surface area becomes 31.06 124.242(2.15) - A(r)= (2.15) 86.83 in2

fullscreen
Step 3

Therefore, the radius of the minimized surface area 86.83...

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in

Math

Calculus

Sorry about that. What wasn’t helpful?