If the volume of a sphere is increased by 95 5/16% without changing the shape, what will be the percentage increase in the surface area?

1 Answer
Apr 26, 2018

Answer:

#color(blue)(56.25%)#

Explanation:

First we observe that, for similar figures. If a similar figure is increased by a scale factor #a/b#, then all linear measurements will increase by #a/b#. Quadratic measurements will increase by a factor #(a/b)^2# and cubic measurements will increase by a factor #(a/b)^3#.

We require an increase of #1525/16%=61/64#:

#61/64#

Remember this will give us #1525/16%#, we need to add #100%# to this.,the #100%# is the amount we have before adding #1525/16%# to it. So:

#1+61/64=125/64#

Now this is volume, so:

#(a/b)^3=125/64#

#a/b=root(3)(125/64)#

We require the scale factor for area.So:

#(a/b)^2=(root(3)(125/64))^2#

If we now subtract 1 form this, we will get the increase in area percentage:

#(root(3)(125/64))^2-1=0.562500000#

This is:

#56.25%#