7th grade math...?

Question

I've been doing homework since I got home from schoo.
Research for a project, science homework,7 page book report,history outline,blah.
Now it's 10 something and I really need to get some sleep.
I need help with a couple of questions that are on my math homework.
1. What is the radius of a cylinder with a height of 18.5 in. and a surface area of 1120.98 inches?
2. what is the radius of a cylinder with a height of 4.2 m. and a surface area of 1808.64 cm.
3. Determine the dimensions and the volume of the largest cylinder that can be placed inside a box that has dimensions 14 in. by 7 in. by 2 in. Explain your reasoning. How much extra space is there inside the box?
4. A cylindrical barrel 3 feet high has a base with radius of 18 inches. You are filling the barrel with sand. If the sand weighs 0.86 ounces per cubic inch and the empty barrel weighs 5 pounds, what will the total weight be when the barrel is full.

Answer 1

The surface area of a cylinder is the surface of the top, bottom and curved side around it. You can calulate this out to be 2pi*r*h + pi*r^2, or 2pi*r(r+h).

So just plug in the remaining numbers and solve:

1. Area = 2pi*r(r+h)
1120.98 = 2pi*r(r+18.5)

Using 3.14 for pi and dividing both sides by 2pi:

178.5 = r(r+18.5)
r^2 - 18.5r -178.5 = 0

Solve this for r using something like the quadratic formua (hint: if you multiply both sides by 2, you can get rid of the decimal during the calculations).

2. Use the formula again and solve for r. Don't forget to first convert the centimeters to meters so that everything is in the same unit.

3. The volume of a cylinder is V = pi*(r^2)h. The biggest side is the 14x7 side of the box, so we want the circle of the cylinder to go up against here. The biggest the diameter could be is 7". So the height can only go as far as the box's third dimension, meaning 2". Therefore we need to find the volume of a cylinder with a radius of 7/2 inches and a height of 2 inches. Once we have this, we can find the volume of empty space by subtracting the cylinder's volume from the box's volume (14*7*2).

4. Find the volume of the barrel given the height and radius, using the volume formula I wrote in #3. Don't forget to convert everything to inches first! Now that you have the volume in cubic inches, multiply this by 0.86 to get the weight of the sand. Finally, add 5 to this number to get the total weight.

Answer 2

I'll do part of it for you, and you should be able to get the rest. If this is homework, you should be able to work through it yourself if you are going to learn how to do it.

1. The surface area of a cylinder is A = 2 * pi * r * h, not including the two ends. To solve for r, just plug in 18.5 in for h, 1120.98 for area A. If you're also including two ends, then the area A = 2 * pi * r * h + 2 * pi * r^2

3. The volume of a cylinder is V = pi * r^2 * h. The three possible ways that you can orient the cylinder in the box will give you the possible dimensions of the cylinder in each case. Calculate and compare. The volume of a box is Length x Width x Height.

Answer 3

1. Surface area of a cylinder = (Area of its base) * (Its height)
So, 1120.98 = (2*pi*radius)*18.5
i.e., radius = 9.64 inches

2. Same as the 1st one.

3. Since the height of the box is 2 in., so the max height of the cylinder that can be placed inside is 2 in.
Also, max length of the box would be 14 in. ('coz 14>7)
So, Volume of the largest cylinder that can be placed inside the box=(Max. possible base area)*(Max. possible height)
i.e., Max possible volume=(2*pi*2)*14 = 175.93 cubic inches.

Extra space inside the box = (volume of the box) - (volume of the largest cylinder) = (14*7*2)-(175.93) = 20.07 cubic inches

4. Volume occupied by the sand inside the barrel = Volume of the barrel (since the barrel is fully loaded with sand)
=pi * 18^2 * (3*12) = 4071.5 cubic inches

Now, weight of the sand per cubic inch = 0.86 ounces
So, weight of 4071.5 cubic inches of sand=4071.5*0.86 ounces
=3501.5 ounces

Therefore, total weight of the barrel = (Weight of the empty barrel)
+ (Weight of sand in it) = 5 lb. + 3501.5 oz. (Do the converting of lb. into oz. yourself)

Answer 4

Shame on you leaving the math for last, you also need to manage your time more wisely. I seriouly doubt that all this work was assign for one night, if so parents and the teachers need to have a heart to heart. (I teach 7th grade, so I can say this)

always write the formula down! (do you have a reference sheet or list of formulas? if not you need to get one)

substitute in what you know (the given #'s for the correct variables)

simplify

solve for the unknowns.

# 3 is a tough one
first find the vol of the box

#4 be sure to convert all units so they are the same

Answer 5

it depends. when i was in 7th grade, some kids were advanced and were doing algebra 1, and some were doing prealgebra like me. im now 17 and going into precalc. everyone is always worried about math because we think its going to be super hard. but, when the teacher teaches it, it wont seem so hard because u will be learning it little by little, not all at once. good luck!

Answer 6

Juan, little man, leave this homework for tomorrow morning and copy from someone elses work. arrive early, now go sleep. I did this and it usually works 70% of the time, worth trying.

Answer 7

Go into school early to ask your teacher. You should do your own homework.

Answer 8

well what you do is go to the techer and ask for help ok iam in 7 grade and if i have a prblem i ask for help