Question 1194061
.
The surface areas of two similar figures are given below. The volume of the smaller figure is also given. What is the volume of the larger figure?
Solid #1
SA= 8yd^2
V= 17yd^3

Solid #2
SA= 128yd^2
V= ?
Volume of the larger figure = ?yd^3
~~~~~~~~~~~~~


<pre>
The ratio of surface areas is  {{{128/8}}} = 16  (the larger to the smaller).


Hence, the ratio of linear dimensions is  {{{sqrt(16)}}} = 4.


It means that the ratio of volumes is 4^3 = 64.


Hence, the volume of the larger body is 64 times the volume of the smaller body, i.e.


    V = 64*17*yd^2 = 1088yd^2.      <U>ANSWER</U>
</pre>

Solved, answered and explained.