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Bobs Math Question: The Official Answers

Bobs Math Question: The Official Answers

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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 :)

 

  • Cubic Feet!!!! Tell me US schools arent still using Imperial measurements in 2005?
  • 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
  • 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
  • i cant understand your answers!
  • 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.
  • what is the answer for 12 and the exponent is 100?
  • 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
  • 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.
  • how many ounces are in 120ml?
  • how many ounces are in 120ml?
  • 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-.
  • 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.
  • Y=1/2X + 2
    CAN YOU DO THE GRAPH FOR THIS ?
  • 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
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