Question

I am very confused as to how you would solve for this questions; please help! We know the original radius of the main show tank is equal to 70 feet. I found the volume to be 359006.67 ft^3

The theme park company is building a scale model of the killer whale stadium main show tank for an investor's presentation. Each dimension will be made 6 times smaller to accommodate the mock-up in the presentation room. How many times smaller than the actual volume is the volume of the mock-up?

Answer 1

Let's assume that the tank is cylindrical in shape. We'll need to know the height as well as the radius.

h=?
r=?

Formula for the volume of a cyl. tank of radius r and height h?

show how you calculated the volume of the orig. tank.

Next, multiply the radius by (1/6) and the height by (1/6). Using these new dimensions (dimensions of the model tank), re-calculate the volume (that is, the vol. of the model).

Now find the ratio of the actual volume to the mockup (model) volume. It will probably be a 1- or 2-digit number greater than 1 but less than 10. But show your work.

Answer 2

@mathmale the shape of the tank is a quarter sphere

Answer 3

The original volume I had calculated is correct, I'm just really unsure what equation to use to solve (if there is one) @mathmale

Answer 4

Thanks for sharing that. This fact should have been part of your original presentation of the problem at hand.

Find the formula for the volume of a sphere of radius r.

Now replace "r" with "(r/6)." Re-calculate the volume.

As before, compare the two volumes. State the multiplier that indicates how many times greater the actual tank volume is in comparison to the mockup volume.

Answer 5

Alright! So, basically my equation would look like v=3/4(3.14)(11.67)^3 ? @mathmale

Answer 6

Please use letters, not numbers, in presenting the formula.

The volume of a sphere is \[V _{sphere}=(\frac{ 4 }{ 3 }) \pi r^3\]

Answer 7

...where r is the radius of the sphere.

What is the radius of the original sphere?

What is (1/6) of the radius of the original sphere?

What are the volumes of the two spheres?

What is the ratio of the larger vol. to the smaller vol.?

Answer 8

Even tho' the tank is in the shape of a quarter sphere, you don't have to bother dividing the sphere volumes by 4. Just find the volumes of the two whole spheres and then find the ratio of these volumes, as directed above.

Answer 9

The original radius of the sphere is 70 feet and 1/6 of the radius would be 11.67 feet. The original volume of the quarter sphere is 359006.67 ft^3. Back to my original question- I was just unsure what to plug in to find the answer.

could you check what I have so far please?
V=4/3(3.14)(11.67)^3
V=6653.971752
I just calculate the new volume after reducing the original radius

now I divide the original volume by the new volume (???)
359006.67/6653.97= 53.95

If I am correct, does this mean it is 54 times smaller??
@mathmale

Answer 10

I haven't actually done the problem myself, but your presentation and your reasoning are sufficiently clear to make your result appear acceptable. We could say, "the mockup tank has a volume that is one fifty-fourth of the actual tank. That 6^3 really reduces the scale!

Answer 11

Hold. Here's what I did to check your results: Ignoring the (4 pi/3) factor, I found 70^3 and 11.67^3 and then divided the smaller into the larger. My result was 216, rounded up from 215.81. Please go through your calculations again and see if you can find anything that explains the discrepancy (216 instead of 54).

Answer 12

Okay, thank you so much! @mathmale

Answer 13

My great pleasure!