Answer :
To find the inner radius of a cylindrical shell, set up simultaneous equations using the given surface area difference and volume. Solve these to find the value of the inner radius.
We need to find the inner radii of a cylindrical shell, given the difference in surface areas between the inner and outer surfaces and the volume of metal used. Let's denote the inner radius by r, the outer radius by R, and the length of the cylinder by h. The difference in the surface areas of the two cylinders (ignoring the top and bottom) can be illustrated by [tex]2\(\pi\)h(R-r)[/tex] which is equal to 88 cm2. The volume of the cylindrical shell is the difference in the volumes between the two cylinders, which can be represented by[tex]\(\pi\)h(R2 - r2)[/tex]and is given as 176 cm3.
The height of the cylinder, h, is given as 14 cm. Therefore, we can set up the following equations based on the given information:
[tex]\(\pi\)\(14\)(R2 - r2)[/tex] = 176 (volume equation)
[tex]2\(\pi\)\(14\)(R - r)[/tex]= 88 (surface area difference equation)
Solving these simultaneous equations allows us to find the value of r. However, without the exact values of R and r, we cannot solve this problem directly here but rather guide on the approach to solving these equations logically.
