Can you please help me with my math homework and give the answers and explanation why the answer is what it is? Please! Thanks & God bless you!
Note- I'm in 7th grade
20-
Carlos wants to build a circular hot tub with a volume of 1,000 cubic feet. What is a good approximation for the radius of the tub?
21-
Carlos decides he would rather build a rectangular hot tub that is 4 ft high and holds 400 cubic feet of water. What would the dimensions of the base of Carlos' hot tub be?
22- A popcorn vendor needs to order popcorn boxes. The vendor must decide between a cylindrical box and a rectangular box.
•The cylindrical box has a height of 20cm and a radius of 7cm.
•The rectangular box has a height of 20cm and a square base with 12cm sides.
•The price of each box is based on the amount of material needed to make the box.
•The vendor plans to charge $2.75 for popcorn regardless of the shape of the box.
a- make a sketch of the boxes and label the dimensions.
B- Find the volume and surface area of each box
C- which box would you chose? Give the reasons for your decision. What additional information may be needed to help you make a better choice?
Note- I'm in 7th grade
20-
Carlos wants to build a circular hot tub with a volume of 1,000 cubic feet. What is a good approximation for the radius of the tub?
21-
Carlos decides he would rather build a rectangular hot tub that is 4 ft high and holds 400 cubic feet of water. What would the dimensions of the base of Carlos' hot tub be?
22- A popcorn vendor needs to order popcorn boxes. The vendor must decide between a cylindrical box and a rectangular box.
•The cylindrical box has a height of 20cm and a radius of 7cm.
•The rectangular box has a height of 20cm and a square base with 12cm sides.
•The price of each box is based on the amount of material needed to make the box.
•The vendor plans to charge $2.75 for popcorn regardless of the shape of the box.
a- make a sketch of the boxes and label the dimensions.
B- Find the volume and surface area of each box
C- which box would you chose? Give the reasons for your decision. What additional information may be needed to help you make a better choice?
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20) Assume the tub is cylindrical and has a height of 3 feet
V = (pi)(r^2)(h)
1000 = (pi)(r^2)(3) let pi = 22/7
1000 = 9.43r^2
1000/9.43 = r^2
106 = r^2
r = SQR(106) ~ 10.3 feet (positive root)
21) Volume of a rectangular solid:
V = LWH
400 = LW(4)
400/4 = LW
100 = LW
A square base 10ft x 10ft will work.
Any rectangle where LW = 100ft^2 will work.
Such as:
20ft x 5ft
15ft x 6 2/3ft
22) Let pi = 22/7
Cylindrical surface area = (pi)(r^2) + (2)(pi)(r)(h)
SA = 22(49)/7 + 22(2)(7)(20)/7 = 154 + 880 = 1034cm^2
Rectangular box surface area = base + 4sides
SA = 12^2 + 4(12)(20) = 144 + 960 =1104cm^2
The cylinder uses less material
You would want to compare the volume of the two boxes:
Cylinder V = (pi)(r^2)(h) = (22/7)(49)(20) = 3080cm^3
Rectangular V = base area(height) = (12^2)(20) = 2880cm^3
It depends on how much the cost savings of material for the cylindrical box vs the cost of an extra 200cm^3 of popcorn in a full rectangular box.
- .--
V = (pi)(r^2)(h)
1000 = (pi)(r^2)(3) let pi = 22/7
1000 = 9.43r^2
1000/9.43 = r^2
106 = r^2
r = SQR(106) ~ 10.3 feet (positive root)
21) Volume of a rectangular solid:
V = LWH
400 = LW(4)
400/4 = LW
100 = LW
A square base 10ft x 10ft will work.
Any rectangle where LW = 100ft^2 will work.
Such as:
20ft x 5ft
15ft x 6 2/3ft
22) Let pi = 22/7
Cylindrical surface area = (pi)(r^2) + (2)(pi)(r)(h)
SA = 22(49)/7 + 22(2)(7)(20)/7 = 154 + 880 = 1034cm^2
Rectangular box surface area = base + 4sides
SA = 12^2 + 4(12)(20) = 144 + 960 =1104cm^2
The cylinder uses less material
You would want to compare the volume of the two boxes:
Cylinder V = (pi)(r^2)(h) = (22/7)(49)(20) = 3080cm^3
Rectangular V = base area(height) = (12^2)(20) = 2880cm^3
It depends on how much the cost savings of material for the cylindrical box vs the cost of an extra 200cm^3 of popcorn in a full rectangular box.
- .--
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Geometry. Eww. Sorry can't help.