Math Please help can anyone help?

Question

1. An open-top box is to be constructed from a 6 foot by 8-foot rectangular cardboard by cutting out equal squares at each corner and folding up the flaps. Let x denote the length of each side of the square to be cut out.

a) Find the function V that represents the volume of the box in terms of x.




2. The volume of a cylinder (think about the volume of a can) is given by V = πr2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 100 cubic centimeters.

a) Write h as a function of r. Keep "" in the function's equation.

b) What is the measurement of the height if the radius of the cylinder is 2 centimeters? Round your answer to the nearest whole number.

Answer 1

V is area of base times height. when you fold sides up, height is x. Length of base is 8-2x and width is 6-2x, so volume is

x(8-2x)(6-2x) = 48x -28x² + 4x^3

V = 2πr²h = 100
r²h = 50/π
h = 50/(πr²)

if r = 2,

h = 50/(4π) = 25/(2π) ≈ 3.98 cm

Answer 2

When you cut x feet off each corner the new length and width are (6 - 2x) and (8 - 2x) and the height will be x. Volume = length X width X height so do that out.

To solve V = πr2h for r, first divide both sides by πh which gives you r squared, then square root both sides. You don't need to put plus or minus because r is always positive.

To solve V= πr2h for h, divide both sides by πr2. Use this formula for 2b

Hopefully you can use this to get the answer, or wait til someone does the whole thing for you!

Answer 3

Along the log axis, 8 will be reduced in length by 2x. The short axis will also be reduced in the same fashion. The volume of the box is the length times width times height, or:

Volume = x(8-2x)(6-2x)

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If V = PI*r^2*h then

h = V/(PI*r^2)

if V = 100 and r = 2 then

100 = PI*4*h
h = 100/PI*4 = 25/PI = 8 (approx.)

Answer 4

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Answer 5

a)
height = x
length = 8 - (x+x) = 8 -2x
breadth = 6 - (x+x) = 6- 2x
volume = x*(8-2x)*(6-2x) ft^3

b) the second question is pretty simple, you just have to substitute the values and solve for h

Answer 6

6-2x = width
8-2x= length
x = depth
V=(6-2x)(8-2x)x
V=48x-28x^2 +4x^3

2. a. h=V/pir^2=100/pir^2

b. h=100/4pi= 25/pi =8