Adventures in maths. Surface Area and Mass calculations.

**MrFlaneur** · 04-27-2011, 01:54 PM

Just got back from college night school. My friendly ENTP teacher took me aside and tried to explain it to me, but after a point I got the impression he was becoming rather pissed off.

Two ball looking things, both made of the same stuff, both proportional in dimensions.

Ball thing A. Surface Area 50cm^2, Mass 500g.
Ball thing B. Surface Area 18cm^2, Mass unknown.

What is the mass of B?

He briefly gave me some ideas about ratios and roots and mass is similar to volume, but it didnt really sink in and im quite lost.

Any ideas?

**Akzis** · 04-27-2011, 01:58 PM

Find the radius of both spheres and then find the ratio/correlation and then simply multiply 500g by the ratio.

**MrFlaneur** · 04-27-2011, 02:03 PM

its not a perfect sphere but they are proportional. Look identical different size. they are spheres but with a bit sliced out so that they sit on a flat base, a bit like a punctured foot(soccer)ball. No other dimensions were given other than whats been written in the first post.

**Aronnax** · 04-27-2011, 03:43 PM

Do you know where the flat area is located relative to the sphere? Are the "balls" 3/4 flat, half flat ect...

**MrFlaneur** · 04-27-2011, 04:09 PM

To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

post 666 *gulp!*

**Solander** · 04-27-2011, 05:12 PM

A long time since I tackled a maths problem. Here's my best shot (criticism invited):

The object has been scaled down from A to B. Imagine you had to say how big the scaling factor was...you could measure the diameter of each. This is the amount the size has changed linearly.

For a linear change x, the area change is x^2, the volume change x^3.

You've only been given measures of the area of each, so begin by taking the sq rt of each.

50 gives 7.071...
18 gives 4.24...

Take the cube of these linear scaling factors to get how much the volume has changed.

The first gives 353.55...
The second gives 76.36...

Now you know that 353.55.. gives you a mass of 500 grams. All you have to do now is multiply 76.36 by the same figure that you would multiply 353.6 by to get 500, ie. 500/353.6 = 1.414...

76.36 * 1.414 = 108 grams

04-27-2011, 01:54 PM	#1
MrFlaneur Veteran Member [55%] MBTI: INTj Join Date: Dec 2007 Posts: 2,205	Just got back from college night school. My friendly ENTP teacher took me aside and tried to explain it to me, but after a point I got the impression he was becoming rather pissed off. Two ball looking things, both made of the same stuff, both proportional in dimensions. Ball thing A. Surface Area 50cm^2, Mass 500g. Ball thing B. Surface Area 18cm^2, Mass unknown. What is the mass of B? He briefly gave me some ideas about ratios and roots and mass is similar to volume, but it didnt really sink in and im quite lost. Any ideas?
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04-27-2011, 01:58 PM	#2
Akzis Member [36%] MBTI: INTP Join Date: Apr 2010 Posts: 1,450	Find the radius of both spheres and then find the ratio/correlation and then simply multiply 500g by the ratio.
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04-27-2011, 02:03 PM	#3
MrFlaneur Veteran Member [55%] MBTI: INTj Join Date: Dec 2007 Posts: 2,205	its not a perfect sphere but they are proportional. Look identical different size. they are spheres but with a bit sliced out so that they sit on a flat base, a bit like a punctured foot(soccer)ball. No other dimensions were given other than whats been written in the first post.
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04-27-2011, 03:43 PM	#4
Aronnax Core Member [103%] MBTI: INTJ Join Date: Apr 2008 Posts: 4,142	Do you know where the flat area is located relative to the sphere? Are the "balls" 3/4 flat, half flat ect...
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04-27-2011, 04:09 PM	#5
MrFlaneur Veteran Member [55%] MBTI: INTj Join Date: Dec 2007 Posts: 2,205	To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts. post 666 gulp!
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04-27-2011, 05:12 PM	#6
Solander New Member [01%] MBTI: INTJ Join Date: Apr 2011 Posts: 15	A long time since I tackled a maths problem. Here's my best shot (criticism invited): The object has been scaled down from A to B. Imagine you had to say how big the scaling factor was...you could measure the diameter of each. This is the amount the size has changed linearly. For a linear change x, the area change is x^2, the volume change x^3. You've only been given measures of the area of each, so begin by taking the sq rt of each. 50 gives 7.071... 18 gives 4.24... Take the cube of these linear scaling factors to get how much the volume has changed. The first gives 353.55... The second gives 76.36... Now you know that 353.55.. gives you a mass of 500 grams. All you have to do now is multiply 76.36 by the same figure that you would multiply 353.6 by to get 500, ie. 500/353.6 = 1.414... 76.36 * 1.414 = 108 grams
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