A ball grow without changing shape. The radius of a sphere grows by 85%. Determine the percentage relationship between surface area and volume has changed. ?

Question

goformit100 · Answer

use unitary method

anonymous · Answer

how? never used it before :(

dumbcow · Answer

85% growth is equal to a growth factor of 1.85

new radius = 1.85r

plug that into surface area and volume formulas for radius

anonymous · Answer

When ball was in its initial stage:$$Surface Area(a) = 4 \pi r^2$$$$Volume(v) = \frac{ 4 }{ 3 }\pi r^3$$radius 'r' grows by  85% i.e $$R =  \frac{ 85 }{ 100 }\times r + r = 0.85r + r = 1.85r$$where 'R' is the varied r.

Now,$$Surface Area(A) = 4 \pi (1.85r)^2$$$$Volume (V) = \frac{ 4 }{ 3 } \pi (1.85r)^3$$
To find the percentage relationship just divide the new "A" by "a" and multiply it by 100%. Same process to get the change in volume in percentage.

anonymous · Answer

Thanks If r=5  
$$4\pi(1.85r)^{2} = 4\pi(1.85 x 5)^{2} = 1075$$

anonymous · Answer

is this wrong?

anonymous · Answer

r =5 I get for (a) 314 (v) 523  (A) 1075 (V)2486   when i divide it i get for a 4.42 and v 4,75, when multiplying by 100 get to big numbers ?

anonymous · Answer

Except, the varied Volume(V), all are correct. Link for varied volume (V) calculation: http://www.wolframalpha.com/input/?i=%284%2F3%29+pi+%281.85*5%29^3