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!! I need it for my homework that I will eventually have to turn in and I will lose a LOT of points if I don't do every problem. Somebody plz clear this up (no one has been able to yet), I'll GREATLY appreciate it!
a and b are correct
c) V = (4s)^3 - pi*s^2*48
= 64 s^3 - 48 pi s^2
= 16 s^2 (4 s - 3 pi)
d) Plug s = 15 into the above equation for the answer
Thank you very much! I really appreciate your help!
Help Me Woodie!
-4x^2+2x-1
Let's go through each part and explain the steps.
a) To find the volume of the cube, you need to multiply the length, width, and height of the cube. In this case, the length, width, and height are all 4s. So, the formula for the volume of the cube in terms of s is V = (4s)^3. You squared 4s because you need to multiply it by itself three times to get the volume.
b) The volume of a cylinder is given by the formula V = pi * r^2 * h, where r is the radius and h is the height of the cylinder. In this case, the radius of the cylinder is s and the height is 48 inches. So the formula for the volume of the cylinder in terms of s is V = pi * s^2 * 48.
c) To find the volume of the metal left after the cylinder is removed, we need to subtract the volume of the cylinder from the volume of the cube. So the formula would be V = (4s)^3 - pi * s^2 * 48. The minus sign represents the subtraction operation.
d) To factor the formula from part (c), you need to look for common factors among its terms. In this case, you can factor out 16s^2 from both terms. So the factored form of the formula is V = 16s^2(4s - 3pi).
e) To find the volume V in cubic inches for s = 15 inches, you simply substitute the value of s into the formula from part (d). So V = 16(15)^2(4(15) - 3pi).
I hope this explanation clarifies the problem for you! Let me know if you need any further assistance.