Ok, this is pretty long, so bear with me.
The problem says:
The diagram (not shown here, sorry) shows a cube of metal with a cylinder cut out of it. The formula for the volume of a cylinder is V=pi*r^2*h, where r is the radius and h is the height.
The cube's length, width, and height is 4s for each one of them. The cylinder's radius is s and the height is 48 inches.
a. Write a formula for the volume of the cube in terms of s. I got V=(4s)^3
b. Write a formula for the volume of the cylinder in terms of s. I got V=pi*s^2*48
c. Write a formula in terms of s for the volume V of the metal left after the cylinder is removed. So wouldn't it be [volume of cube]-[volume of cylinder]=V? If so, I got (4s)^3-pi*s^2*48=V. Is this correct? If it isn't, then that would explain my problem for this next one...
d. Factor your formula from part (c). I couldn't find out how to factor this one out. No other numbers in the polynomial can be divided by pi evenly, so what do I do?
e. Find V in cubic inches for s=15 in. I haven't gotten to this one yet, but I'll probably figure it out soon.
I really need help!! Somebody plz clear this up, I'll GREATLY appreciate it!
I'm here to help! Let's go through each part of the problem step by step.
a. Yes, you are correct. The formula for the volume of a cube is V = (4s)^3, where 4s represents the length, width, and height of the cube.
b. Again, you are correct. The formula for the volume of a cylinder is V = pi * s^2 * 48, where s represents the radius and 48 represents the height.
c. To find the formula for the volume of the metal left after the cylinder is removed, you need to subtract the volume of the cylinder from the volume of the cube. So, the correct formula should be: V = (4s)^3 - pi * s^2 * 48.
d. To factor the formula from part (c), we need to look for common terms that can be factored out. In this case, the common term is s^2. So, we can rewrite the formula as: V = s^2 * [(4s)^3/s^2 - pi * 48]. Simplifying further, we get: V = s^2 * [64s^3/s^2 - 48pi]. Now, we can simplify the term inside the square brackets: V = s^2 * [64s - 48pi].
e. To find V in cubic inches when s = 15 inches, simply substitute s = 15 into the formula we obtained in part (d). Thus, V = 15^2 * [64(15) - 48pi]. Now, you can calculate the value of V by evaluating this expression using the value of pi (approximated as 3.14159) and performing the necessary calculations.
I hope this clarifies things for you! Let me know if you have any further questions.