I am doing a project, are my answers correct?
1. Find and simplify the volume-to-surface-area ratio for each of the three possible ice cube shapes. You can use this chart.
|Shape| S/A Formula|Volume Formula
Cube | S.A=6s^2 | V=s^3
6/s
Sphere|S.A+4 pi r^2|V=4/3 pi r^3
3/r
Cylinder| S.A=2 pi r^2+2 pi rh |V= pi r^2 h
2/h + 2/r = 2 (r+h)/rh
2. Use the ratios to choose the best shape for an ice cube—a cube, sphere, or cylinder. Also, choose what you think is the best size for that shaped ice cube.
A cylinder is the best shape for an ice cube.
3. Consider these questions as you make your decision:
a. Since the purpose of an ice cube is to keep a drink cold, is it better for an ice cube to have a high volume or a low volume?
Low volume
b. Since heat touching the surface of an ice cube causes it to melt, is it better for an ice cube to have a large surface area or a small surface area?
You would want to have the least surface area.
c. Which volume-to-surface-area ratio would be better for an ice cube— the lowest possible or the highest possible?
Lowest possible
d. How does increasing the size of an object affect its volume-to-surfacearea ratio?
4. Create a visual model to show your ice cube design, including the dimensions you would choose and the volume and surface area of that cube.
(picture of a cylinder)
Surface Area = 2(pi r 2) + (2 pi r)* h
why is Connexus so hard tho? Like get an A on a unit test nothing happens fail 1 quick check ur A goes down to a D
ConnexusTeacher I think you forgot the part where you are a student
this was probably the most unhelpful post ive ever read. literally half the responses are just people arguing.
here's what i found, but there's a good chance i'm wrong, so don't stake your life or your grades on it. do a little fact checking first:
1. it wants you to find volume-to-surface-area ratio for all the shapes.
an ice cube's dimensions are about 7/8 of an inch tall and 1 and 1/8 inches wide. you really only need that 1 and 1/8 inch for the formula.
take your 1 and 1/8 inch and convert it to a decimal to get 1.125 inches, but you can round that up to 1.13 inches.
pop that number into the google surface area calculator, and here are the results: A= 6s^2 = 6·1.13^2 = 7.59
now we find the volume of the cube. we need the length, width, and height for volume.
length of an ice cube: 1 and 1/4 inch/1.25 inch
width of an ice cube: 1 and 1/8 inch/1.13 inch
height of an ice cube: 7/8 inch/ 0.875 inch
1.25*1.13*0.875= 1.235
simplify a little, and the volume of the ice cube should be about 1.24 inches
so, the volume-to-surface-area-ratio for the ice cube is about 7:1
for the sphere: the average ice sphere has a diameter of 2 inches, which means the radius is 1 inch.
A= 4πr^2 = 4·π·1^2 ≈ 12.57
surface area of ice sphere ≈ 12.57
for the volume, you can't exactly use length, width, and height on a sphere, so we turn again to the google calculator.
V= 4/3πr^3 = 4/3·π·1^3 ≈ 4.19
the ratio is about 12:4
now, cylinder:
dimensions of an ice cylinder: about 2 inches by 2.75 inches
Surface Area- A= 2πrh+2πr^2 = 2·π·1·2.75+2·π·1^2 ≈ 23.56 (im not 100% sure on this calculation, so please check it before you use it)
Volume- V= πr^2h = π·1^2·2.75 ≈ 8.64
the ratio, if i'm correct, should be about 23:8 (this sounds kind of wrong to me though, so maybe redo the cylinder calculations on your own)
so, the volume-to-surface-area ratio for all the shapes should be this:
cube- 7:1
sphere- 12:4
cylinder- 23:8
2. choose the best shape for ice in drinks (i'd go with the cube, but you make your own decisions)
3. here they have some questions for you to think about to make your decision. we'll go over them real quick.
a. Since the purpose of an ice cube is to keep a drink cold, is it better for
an ice cube to have a high volume or a low volume?
from what i've read, low volume is best because it keeps the drink cold but doesn't water down the flavor too much.
b. Since heat touching the surface of an ice cube causes it to melt, is it
better for an ice cube to have a large surface area or a small surface
area?
again, i'd say small surface area so that there isn't too much extra water in your drink that messes with the flavor
c. Which volume-to-surface-area ratio would be better for an ice cube—
the lowest possible or the highest possible?
lowest possible so that the ice doesn't melt right away and so that the drink will stay cold
d. How does increasing the size of an object affect its volume-to-surface-area ratio?
making the object bigger makes the ratio bigger because the numbers you have to calculate will be larger
4. Create a visual model to show your ice cube design, including the dimensions you would choose and the volume and surface area of that cube.
you'll have to do this bit on your own. basically it just wants you to go into paint 3D and make a picture of a cube, sphere, or cylinder, and then put some numbers on it.
use your own judgement for what dimensions the ice shape of your choice should be. the dimensions i used to make the ratios are the average size of the ice shapes. you can make the shapes larger or smaller, but you may have to do some extra math to keep the ratios proportionate.
i tried my best on this. it's most likely not 100% correct, but i did try. i hope it helped at least a little.
Alicia you got here somehow to so don't even act like you didnt get here from searching it bc how else did you get here?
But why go to all the fuss of making spherical ice cubes? What’s wrong with regular ice cubes? The answer is surface area to volume ratio: the volume of the ice provides the cooling effect but the surface area controls how fast the ice melts – the lower the surface area to volume ratio the longer the ice will take to melt for the same cooling effect. Essentially, a lower surface area to volume ratio keeps your drink cold, but stops it from becoming too diluted.
A cube with sides of length x will have a volume of x3 and a surface area of 6x2. The surface area to volume ratio for a cube is therefore 6 to 1 (6:1). Of all the Platonic solids (solids with identical faces) the icosahedron has the lowest surface area to volume ratio.
help i guess ITS A CONNEXUS SCHOOL PROBLEM ITS NOT LITERal
The volume of a cube is defined as
V = s^3
The surface area of 3 cubes:
SA = 3*6s^3
SA = 18s^3
The volume of 3 cubes
V = s^3
V = 3s^3
Volume-to-surface-area ration
Ya guys some of you don't go to our school its a Connexus or connections academy problem
no it wasn't
#1 you did the area:volume ratio. It asked for volume:area. So, flip all your fractions.
#2 why did you choose cylinder? What makes it "best"?
#3 justify using your criteria. You might want to consider rapid cooling or prolonged chilling effect.