Bobs Math Question: The Official Answers


EDIT: Please note: This is a single post explaining the answer to a question posted earlier on this blog. 

This site is NOT intended as a general purpose site in which to get help with your math homework.

If you’re having problems with your math homework, then you should consider asking your parents for help, you’re not likely to find it here, sorry about that.

 


Ok, he’s back 🙂  My last post was a math problem that the teacher in my wife’s classroom gave to the students (mostly 11 and 12 year olds fwiw).

Here’s the official answer to the problem, the kids needed to show ALL the calculations (sorry for the word-junk):


Pyramid L=W=2’ H2 = 22 – 12 so H = 1.73

V        =1/3*l*w*h

= 1/3*2*2*1.73 = 2.31 cubic feet

SA     =b2 + 2bh

= (2)2 + 2*(2)*1.73

= 4 + 6.92 = 10.92 square feet.

 

Triangles

V=B*h   SA = front + back + 3 sides

= 2*(1/2*l*h) + 3* L*W

Triangle #1 : L=8’, W=2’ H2 = 82 – 42 H = 6.93

V = 1/2*8*6.93*2 = 55.44 cubic feet

SA = 2(1/2*8*6.93) + 3*8*2 = 103.44 square feet

 

Triangle #2 : L=9’, W=2’ H2 = 92 – 4.52 H = 7.79

V = 1/2*9*7.79*2 = 70.11 cubic feet

SA = 2(1/2*9*7.79) + 3*9*2 = 124.11 square feet

 

Triangle #3 : L=10’, W=2’ H2 = 102 – 52 H = 8.66

V = 1/2*10*8.66*2 = 86.6 cubic feet

SA = 2(1/2*10*8.66) + 3*10*2 = 146.6 square feet

 

Base of Tree: L=W=2’  H= 3’

V = L*W*H = 2*2*3 = 12 cubic feet

SA     = 2(L*H) + 2(W*H) + 2(L*W)

          = 2(2*3 + 2*3 + 2*2)

          = 2(6 + 6 + 4)

          = 32 square feet

 

6 cones with H=1’, R=.5’, S= 1.12’

V = 1/3*π*r2h = 1/3 * 3.14*.52 * 1 = .26 cubic feet

Total volume = 6*.26 = 1.56 cubic feet

Volume before cutouts:

Pyramid                    2.31

Triangle #1           55.44

Triangle #2           70.11

Triangle #3           86.60

Base                        12.00

Cones                        1.56

TOTAL                  228.02

                             Cubic feet

 

 

Surface Area before cutouts:

Pyramid                   10.92

Triangle #1           103.44

Triangle #2           124.11

Triangle #3           146.60

Base                        32.00

Cones                      15.30

TOTAL                  432.37

Square

 


Cutout Calculations – Volume

All of the volume of the cutouts are subtracted from the total volume of the Christmas tree.

 

There are 6 cylinders total.

1 has r=1, h=2

4 have r=1.5, h=2

1 has r=2, h=2

 

V = πr2h       SA = 2πr2 + 2πrh

V        = π*(12 + 4(1.52) + 22)*2

          = π*(1+9+4)*2

          = 3.14*14*2 = 87.92 cubic feet

 

Small Triangular Prisms

There are three triangular prisms.

1 has L=B=1 and W = 2’

H2 = 12 – .52 so H= .87’

2 have L=B=1.5 and W = 2

          H2 = 1.52 – .752 so H = 1.69’

 

V        = Bw where B=1/2*l*h

V        = (1/2*1*.87*2) + 2*(1/2*1.5*1.69*2)

          = .87 + 5.07

          = 5.94 cubic feet

 

Total volume to subtract:

87.92

+5.94

93.86 cubic feet

 

Christmas tree volume minus cutouts:

          228.02

          -93.86

134.16 Cubic Feet total


Cutout Calculations – SA

The front and back SA’s are subtracted from the total SA of the Christmas Tree but the side SA’s are added to the total.

 

Cylinders

Front and back SA = 2πr2

Side SA = 2πrh

Front and Back SA

          = 2π(12 + 4*1.52 + 22)

          =6.28 * (1+9+4)

          = 87.92 Square feet

Side SA

          = 2πrh

          =2*π*(1+4*1.5+2)*2

          = 12.56 * 9 = 113.04 Square feet

Small Triangular Prisms

Front and Back SA

= 2*1/2*b*h

= b*h

= 1*.87 + 2(1.5*1.69)

= .87 + 5.07

= 5.91 Square Feet

 

Side SA

          = 3*b*w

          = 3*(1+1.5+1.5)*2

          = 24 square feet

Twice the SA of top of Base

          =2(2*2)=8 Square Feet

 

SA to Add:            137.04

SA to Subtract:      101.83

Total SA to add:      35.21

 

Christmas Tree SA plus cutouts:

          432.37

          +35.21

          467.58 Square Feet Total

Edit: Reduced Google juice of this post by changing the title from “Bobs Math Answers” to something more accurate – this post isn’t intended to be a Q&A for students who are having trouble with their math homework 🙂

 

Comments (22)

  1. Cubic Feet!!!! Tell me US schools arent still using Imperial measurements in 2005?

  2. What is the answer for: Tim brings 2 empty containers one of 7 liters the other of 11 liters to a fountain of water.

    How many operations does he need to fill one of the containers with exactly 6 liters of water? Each operation one container must be completely filled or completely emptied.

    Barry

  3. Jarred says:

    Need Answers To These Following Questions!!!

    Percent And Estimation

    67% of 93

    25% of 63

    92% of 42

    73% of 81

    Estimate 21% of 348

    Estimate each pericent 6 out of 59

    6 out of 35

    9 out of 23

  4. willow says:

    i cant understand your answers!

  5. DWalker says:

    Jarred, the answers are 1, 2, 3, and 4; 21% of 348 is 5; 6 out of 59 is 6; 6 out of 35 is 7; and 9 out of 23 is 8. Hope this helps.

  6. nikki says:

    what is the answer for 12 and the exponent is 100?

  7. Kiliman says:

    Barry, I believe it takes 22 steps.

    Hope this looks ok, since you can’t format comments. The numbers in brackets show the amount of water in each container (7 and 11 respectively).

    Step# Action [7-liter] [11-liter]

    1) Fill 11 [0] [11]

    2) Pour into 7 [7] [4]

    3) Empty 7 [0] [4]

    4) Pour into 7 [4] [0]

    5) Fill 11 [4] [11]

    6) Pour into 7 [7] [8]

    7) Empty 7 [0] [8]

    8) Pour into 7 [7] [1]

    9) Empty 7 [0] [1]

    10) Pour into 7 [1] [0]

    11) Fill 11 [1] [11]

    12) Pour into 7 [7] [5]

    13) Empty 7 [0] [5]

    14) Pour into 7 [5] [0]

    15) Fill 11 [5] [11]

    16) Pour into 7 [7] [9]

    17) Empty 7 [0] [9]

    18) Pour into 7 [7] [2]

    19) Empty 7 [0] [2]

    20) Pour into 7 [2] [0]

    21) Fill 11 [2] [11]

    22) Pour into 7 [7] [6]

    Kiliman

  8. Edward says:

    Might as well give Barry his answer too.

    Container A holds 7 liters

    Container B holds 11 liters.

    Both are empty to start.

    A=0 B=0

    1) Fill A from the fountain

    A=7 B=0

    2) Empty A into B

    A=0 B=7

    3) Fill A again

    A=7 B=7

    4) Fill B from A

    A=3 B=11

    5) Empty B into the fountain

    A=3 B=0

    6) Empty A into B

    A=0 B=3

    7) Fill A from the fountain

    A=7 B=3

    8) Empty A into B

    A=0 B=10

    9) Fill A from the fountain

    A=7 B=10

    10) Fill B from A

    A=6 B=11

    So after 10 steps we have exactly 6 liters in container A.

  9. carl says:

    how many ounces are in 120ml?

  10. carl says:

    how many ounces are in 120ml?

  11. Diana says:

    Please just give me the answer I am so tired of searching. I’m not so good at math so just give me the answer -k-.

  12. Terry says:

    How can i work out the answer.

    QUESTION: A cake is cut into 7 pieces. that means 7 prism,s how many base areas can be counted.

  13. LUIS says:

    Y=1/2X + 2

    CAN YOU DO THE GRAPH FOR THIS ?

  14. Cheyenne says:

    Janet wants to put ribbon around the outside edge of a circular picture. How much ribbon is needed for a picture with a radius of 7.1 inches

  15. what is the monomial answer for 3n to the 7th power/15n to the 3rd power

  16. RJ says:

    Carl, American ounces or British ounces? 😛

    4 in an american, 4.2 in a british 🙂

  17. Brian says:

    Holt’s Model for exponential smoothing is suitable for a time series where the mean of the distribution tends to follow a trend either up or down T F

    2. The Expected Opportunity Loss indicates the maximum amount a decision-maker would be willing to spend to obtain information. T F

    3. A moving-average forecast tends to be more responsive to changes in the time-series data when more values are included in the average. T F

    4. In exponential smoothing, an alpha of 0.3 will cause a forecast to react more quickly to a large error than will an alpha of 0.2. T F

    5. Expected opportunity loss (EOL) will sometimes result in the same decision as the maximum expected monetary value (EMV). T F

    6. Linear regression is the preferred forecasting model when the time series has a probability distribution that is unstable. T F

    7. The next value in a time series cannot be forecasted with certainty because it is a random variable.

    T F

    8. Regarding simple exponential smoothing, when the time series is rather volatile and when “w” is large, the smoothing effect may be minimal. T F

    9. In time series analysis, the long-term directional movement in the series should be determined only after the data has been seasonally adjusted. T F

    10. Residual analysis is a means of determining patterns in time series data that have not been

    modeled. T F

    A. Which of the following is not a criterion for decision making:

    a. EVPI

    b. Maximin

    c. Maximax

    d. Equally likely

    e. Maximum likelihood

    B. Gradual long-term movement in time-series values is called:

    a. Seasonal variation

    b. Trend

    c. Cycles

    d. Irregular variation

    e. Random variation

    C. In order to increase the responsiveness of a forecast made using the moving-average method, the number of values in the average should be:

    a. decreased

    b. increased

    c. multiplied by a larger alpha

    d. multiplied by a smaller alpha

    e. none of the above

    D. Which of the following smoothing constants would make an exponential smoothing forecast equivalent to a last-value forecast?

    a. 0

    b. 0.01

    c. 0.1

    d. 0.5

    e. 1

    E. Which of the following possible values of alpha would cause exponential smoothing to respond the most quickly to forecast errors?

    a. 0

    b. 0.01

    c. 0.05

    d. 0.1

    e. 0.15

    F. Given forecast errors of 5, 0, -4 and 3, what is the mean absolute deviation?

    a. 1

    b. 2

    c. 2.5

    d. 3

    e. 4

    G. Given an actual latest demand of 105, a previous forecast of 97, and an alpha of 0.4, what would be the forecast for the next period using the exponential smoothing method?

    a. 80.8

    b. 93.8

    c. 100.2

    d. 101.8

    e. 108.2

    H. Which of the following is not a type of judgmental forecasting:

    a. Managerial opinion

    b. Sales force composite

    c. Time-series analysis

    d. The Delphi method

    e. Consumer market survey

    I. The primary method for causal forecasting is:

    a. Sensitivity analysis

    b. Linear regression

    c. Moving-average

    d. Exponential smoothing

    e. The Delphi method

    J. A manager uses the equation Y = 40,000 + 150 X to predict monthly receipts. What is the forecast for July if the base month is April of the same year?

    a. 40,450

    b. 40,600

    c. 42,100

    d. 42,250

    e. 42,400

  18. ANNA says:

    Find the sum of three sets of fractions that must equal to 1 using the number 1-9 just once.