Step 6: Applications of the Volume Formula.

We're out there in the real world now. With a handy little toolbox and some useful tips, lets try and tackle some problems...

Imagine you are in the 16th century. Italy. Sitting at the desk of Galileo Galilei. Galileo has given you the task of finding out the volumes of certain planets. He has provided you with the radii of those planets. They are as follows:
Mercury-----2,440,000 metres.
Venus------ 6,051,000 metres.
Mars ----- 11145013.12 feet.
Jupiter----- 78184601.92 yards.

Galileo wants all answers in terms of cubed metres . What answers will you give Galileo?

SPOILER: Watch out for Mars and Jupiter!

Well, since we know the radii ...the problem becomes very simple!
The Answers are:
Mercury---------6.085 multiplied by 10 raised to the power 19.
Venus----------9.28 multiplied by 10 raised to the power 20.
Mars------------1.642 multiplied by 10 raised to the power 20.
Jupiter--------- 1.5306 multiplied by 10 raised to the power 24.
(All values are in cubed metres.)

I have to build a semi- spherical planetarium inside a huge room of volume 63,000 cu.metres. The diameter of the planetarium should be 50 metres. Will my planetarium fit inside the room?

ANSWER: Remember that the planetarium is SEMI-spherical. So it's volume is half the volume that we calculate for a sphere. Half the sphere will quite easily fit inside the room.
Volume of the planetarium=32724.92 cu.metres.

PROBLEM 3) Imagine that one day Mr. Gates, the millionaire goes mad and decides to fund a project in which the moon is to be opened up and completely filled with marbles having circumference 2metres. Now the radius of the moon is 1,738,000 metres. Approximate how many marbles will fit into the moon till the moon fills up completely!

The no. of marbles =(volume of the moon) divided by (volume of each marble).

And radius = (circumference)/ 2*PI

Volume of each marble= 0.1351 cu.metres
Volume of the moon =2.199 multiplied by 10 raised to the power 19.
The no. of marbles =1.6277 multiplied by 10 raised to the power 20!!!

NOTE: Given below, are the tables which summarize all that we have already examined in the steps prior to this one. They may prove to be useful in solving the above problems.

<p>Thank you for this Instructable. It is simple and easy to follow. I was searching all over this website in order to find ways to figure out how to build a frame of a 10 foot sphere and your explanation on the formulas have helped me out in to figuring out or seeing the mathematics portion. Mathematics is not my strongest skill, I am more on the artistic and design side. I've learned that if I can think of it, I can build it. At least most of the time. But I will never disregard that in order to be precise that one, even as an artist, has to have a strong foundation in basic mathematics, especially now that I am working with fractals. Actually, I always have worked with fractals but I never even knew that until it was pointed out to me that I was using fractals for some of my art and designs. Since I learned about fractals I've been more fascinated by their use. Anyhow, thank you again for your Instructable.</p>
you are supposed to do area=pi X (radiusXradius) ,<br/>not area = pi X radius X radius.<br/>
Try that on a calculator.. pi x 10 x 10 is the same as pi x (10x10)
its one of the properties of multiplication
it's the same
Cant that be 3.14 * diameter?<br/><br/>-PKT<br/>
diameter is nothing but twice the radius...so you can write any equation in terms of diameter as well...if i'm not mistaken, you've written the equation of circumference of the circle...it's right...
So, i'm right? -PKT
Yeah...scotty3785 is right.. When multiplication signs are the only signs in an equation, parenthesis rarely matter. Although the issue with matrices is different...
easiest way= make a 2 piece mold of the sphere in clay hardden it fill both halves with water 1ml=1 cubic cm so measure how much water it takes :D
water displacement FTW
V =&nbsp; d x d x d / 1.91<br />
You did a nice job of explaining a hard concept. Now explain integration.
integration would be harder to actually explain..but i'll definately try!
You could try to explain how to find the area of two intersecting spheres then you would need integration and several years differential calculus.
You could just use the disc method to integrate the portions of the intersecting spheres and then add the results. Its not very difficult.
I know.....im really perplexed as to how i can explain the concept of Integration itself ...any suggestions.???
Let's see. Take 3 years and 4 to 5 1,000 page textbooks. Seriously, I think graphing is the way to go. Find the area under a curve using smaller, and smaller (eventually an infinite number of) rectangles. I can't get to my books right now, but I think that's how I was taught. Good luck.. We're all rooting for you.
yaa..thats right i guess that's the simplest way to get it done...i'll try my best...
Why don't you just prove that an integral is an antiderivative? I think its the most straightforward way.
ease up with the exclamation marks :)
Yeah i know i've put too many in there, but dont worry they wouldnt hurt ne1
ya I know :). Hey just wanna say thanks a lot. Your instructable helped me out a lot for a project I had to do for school. thanks! I appreciate it.
Wow! dat's made my day!
Cant you just get the volume by multiplying pi by radius by radius by height of a cylinder of the same dimensions (lets say 2 height and 2 radius) then cut it in half (or third I can't remember) then multiply it by two? I am pretty sure that gets the volume of a cylinder.
Volume of a sphere, the simple way: 4πr² OR four times pi times radius times radius...just find the radius! easy isn't it?
Couldn't you just put it into a graduated flask with water in it and subtract the difference? I think I'm missing the point, sorry.
Yeah...thats right!
A hockey puck is a flat circle, not a sphere.
A hockey puck is technically a right-circular cylinder, not a circle <em>or</em> a sphere.<br/>
It is a sphere if you spin it! GO CONDORS! LOL
I'm not trying to be jerk here,... but it's not even a sphere if you spin it. Yeah, it looks a lot like a sphere, but it's still not. Only a circle rotated about a radial axis will result in a sphere. A right-circular cylinder (a circle extruded through some depth along a line perpendicular to the plane of the circle) rotated about a radial axis will result in something different than a sphere.
There are two kinds of hockey played around the world, ICE hockey is played with a puck, which is as you said , a flat disk. But the other kind, played on a turf field uses a round white colored ball ( which is very much, a sphere)!!!
knektek pi x radius x radius is the same as pi X (radius X radius). It is the associative property.
If it was'nt the associative property...it would've been called common sense!.
Yeah I know, I didn't want to be mean.
for measuring the volume of things like golfballs or a small sphere its easier to use water displacement, measure how much water u have in a measuring cup, put in the sphere, measure how much you have after. the difference = the volume, more accurate for things like golfballs which are not perfect spheres<br/>
True... very correct...i've explained only the theoretical ways of determining volume.
i liked it, we learned area of a circle and a cylinder this year but we didnt do cones or spheres or anything. With the pi*radius*radius, itd be easier to just say &#960;R<sup>2. </sup><br/><br/>This will be pretty cool to learn before grade nine XD<br/>
How do you get that Pi symbol? -PKT
I just copied it off of yahoo answers, i don't think it said how to actually type it though =P<br/>
I downloaded some software..dont remember the name...it enabled me to write equations with ease.
Thanks! You can solve the sum i've posted at the end of the instructable...although it contains values in the powers of ten....you can take any value and try and solve them!
I didn't see a golf ball yesterday =D<br/>
Very funny....ok ...i deleted that bit...but ...overall, how would u rate the instructable?
a 5 because it is very well presented and professional
Thanks a lot!!! Made my day!!! By the way...i tried making "the world's best paper airplane" u posted...i've posted a comment on ur page! Unfortunately ....the plane's noseweight was pretty high...kept on diving!!!
though the pics take a lot of time to load.... they shud hv been smaller!! And the instructable is a bit long...... But I would say helpful too!!
hey fantastic work.keep the nice work......

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