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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 :)
Comments
Anonymous
January 04, 2005
Cubic Feet!!!! Tell me US schools arent still using Imperial measurements in 2005?Anonymous
January 04, 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.
BarryAnonymous
January 05, 2005
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 23Anonymous
January 12, 2005
The comment has been removedAnonymous
January 12, 2005
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.Anonymous
January 14, 2005
what is the answer for 12 and the exponent is 100?Anonymous
January 14, 2005
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]
KilimanAnonymous
January 14, 2005
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.Anonymous
January 20, 2005
how many ounces are in 120ml?Anonymous
January 20, 2005
how many ounces are in 120ml?Anonymous
January 21, 2005
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-.Anonymous
January 22, 2005
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.Anonymous
January 27, 2005
Y=1/2X + 2
CAN YOU DO THE GRAPH FOR THIS ?Anonymous
January 27, 2005
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 inchesAnonymous
January 27, 2005
what is the monomial answer for 3n to the 7th power/15n to the 3rd powerAnonymous
January 27, 2005
The comment has been removedAnonymous
January 28, 2005
The comment has been removedAnonymous
January 29, 2005
Find the sum of three sets of fractions that must equal to 1 using the number 1-9 just once.Anonymous
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