HP42s first major program (Double Integral) Best way to approach?

[DM48]

I am trying to convert a program from my HP48G to my HP42s and DM42.

Background
On the HP, I take three numbers from the stack and store them as local variables and have the equation /->NUM evaluate the expression to a number. It's really easy on the 48G, but slow (seconds to minutes depending on the numbers used. I use the iOS app m48+ to evaluate the expression fixed to five decimals. It computes instantly on my iPhone. I hoping to run this on the DM42 which is pocketable.

48G Stack

3:10
2:12
1:5

Stack Line 3 stores to a
Stack Line 2 stores to b
Stack Line 1 stores to c

Question
What is the best method to approach this double integral on the 42s? Keep in mind that a, b, and c are variables and I run this calc a lot when I run it. May run it over 100 times in one setting.

Example numbers are a (24), b (29), and c (12). The final answer would be multiplied by four giving an answer of 2325.62 for the example numbers.

\(\large I = \int_a^b\int_0^c\frac{r\sqrt{c^2-x^2}}{\sqrt{r^2-x^2}}\;\partial x\;\partial r \)

Any help getting me pointed in the correct direction would be appreciated. I am assuming I need to to solve the inner integral and then the outer integral on the 42s separately. This assumes the 42s doesn't have the same ability to evaluate the expression in the same way as the 48G. Correct?