I am doing volume and surface areas of 3D figures, and am running into the problem of having to give the exact answers as well as approximate answers. The approximate answers I don't have a problem with but the exact answers are requiring me to get the solution of a problem like: Pi x (4in)^2 x 9in. I type it into my calculator and get 452. but the homework is the correct answer is 144pi in^3. I just don't understand what I am missing?
You're doing it right. Exact answer just means to keep your answer in symbolic form-- keep your constants.
pi * 4^2 * 9 = 144pi (exact)
If we wanted the approximate answer, we could substitute pi = 3.14, and then you get 452.
To solve the problem properly, you need to follow the correct order of operations and use the well-known formula for calculating the volume of a cylinder, which is V = πr^2h.
Let's break down the calculation step by step:
1. The formula for the volume of a cylinder is V = πr^2h, where r represents the radius of the base and h represents the height.
2. In your case, the radius (r) is given as 4 inches, and the height (h) is given as 9 inches.
3. To find the volume, substitute the values into the formula: V = π(4in)^2(9in).
4. Begin by squaring the radius: V = π(16in^2)(9in).
5. Simplify the multiplication: V = π(144in^3).
6. Finally, the answer should be written as 144πin^3, not 452.
So, the correct answer is indeed 144πin^3. If your calculator is giving you a different answer, it is most likely due to incorrect input or an error in using parentheses or the π symbol on the calculator. Please double-check your calculations and make sure you are using the correct values and symbols in the calculation.