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Tutors Answer Your Questions about Volume (FREE)
Question 73750: I am stuck on this problem, if someone can be of any assistance I would greatly appreciate. Thank you!
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 the 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.
Answer
b) Graph this function and show the graph over the valid range of the variable x.
Show Graph here
c) Using the graph, what is the value of x that will produce the maximum volume?
Answer
Click here to see answer by jim_thompson5910(28595)  |
Question 73751: 2) The volume of a cylinder (think about the volume of a can) is given by V = πr^2 h 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 "π" in the function's equation.
Answer
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
Show work in this space
c) Graph this function.
Show graph here
"π" is the symbol for (PI)
Click here to see answer by jim_thompson5910(28595) |
Question 74943: The volume of a cylindrical tank is given by the formula V =πh r2
where h is the height of the cylinder and r is its radius. Find the
volume to the nearest tenth of a cubic foot of a cylindrical tank that
has a radius of 3 feet and a height of 5 feet.
A bacteria culture started with a count of 720 at 8:00 A.M., and after
t hours is expected to grow to f(t)=720(3/2)t. Estimate the number of
bacteria in the culture at 11:00 A.M. the same day.
Click here to see answer by funmath(2925) |
Question 82187: Hello everyone,
Find the amount of water, in litres, discharged in 10 minutes from a pipe, 4 cm in diameter measured internally, if the water flows at a speed of 50 cm per second. (pi = 3.14)
Please check to see if I have computed the right answer. Thanks in advance.
-----
My Work:
If the water flows at 50 cm/s and the pipe's diameter is 2 cm, the volume of water being discharged = the volume of water that would fit in a cylinder with a height of 50 cm and radius 2.
Volume of discharging water = (pi)(4)(50)
= 628.32 cm^3
Therefore, 628.32 cm^3/s is being discharged --> 37699.2 cm^3/min --> 376992 cm^3/10 mins.
Since 1 L = 1000 cm^3: 376992 cm^3/10 mins = 376.992 L/10 mins
• In 10 minutes, 376.992 liters of water will be discharged from this pipe.
Click here to see answer by stanbon(57377) |
Question 82476: The volume of a cylindrical tank is given by the formula V=nh r ^2 where h is the hieght of the cylinder and r is its radius. Fine the volume to the nearest tenth of a cubic foot of a cylindrical tank that has a radius of 3 feet and a height of 5 feet.
Click here to see answer by jim_thompson5910(28595) |
Question 83267: The volume of a cylinder is given by v=πr2h
Where r is radius of the cylinder and h is height of the cylinder. Suppose the volume of the cylinder is 100 cubic centimeters.
Write h as a function of r. keep π in the functions equation
Click here to see answer by Mona27(45) |
Question 83038: 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 121 cubic centimeters.
a) Write h as a function of r. Keep "π" in the function's equation.
Answer:
Show work in this space.
b) What is the measurement of the height if the radius of the cylinder is 3 centimeters? Round your answer to the hundredth's place.
Answer:
Show work in this space.
c) Graph this function.
Show graph here.
3) The formula for calculating the amount of money returned for deposit money into a bank account or CD (Certificate of Deposit) is given by the following:
A = P (1 + r/n)^nt
A is the amount of returned
P is the principal amount deposited
r is the annual interest rate (expressed as a decimal)
n is the compound period
t is the number of years
Carry all calculations to 6 decimals on all assignments then round the answer to the
nearest cent.
Suppose you deposit $20,000 for 3 years at a rate of 8%.
a) Calculate the return (A) if the bank compounds annually (n = 1).
Answer:
Show work in this space. Use ^ to indicate the power.
b) Calculate the return (A) if the bank compounds quarterly (n = 4). Round your answer to the hundredth's place.
Answer:
Show work in this space .
c) Calculate the return (A) if the bank compounds monthly (n = 12). Round your answer to the hundredth's place.
Answer:
Show work in this space.
d) Calculate the return (A) if the bank compounds daily (n = 365). Round your answer to the hundredth's place.
Answer:
Show work in this space.
e) What observation can you make about the size of increase in your return as your compounding increases more frequently?
Answer:
f) If a bank compounds continuous, then the formula becomes simpler, that is
where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding. Round your answer to the hundredth's place.
Answer:
Show work in this space
g) Now suppose, instead of knowing t, we know that the bank returned to us $25,000 with the bank compounding continuously. Using logarithms, find how long we left the money in the bank (find t). Round your answer to the hundredth's place.
Answer:
Show work in this space
h) A commonly asked question is, “How long will it take to double my money?” At 8% interest rate and continuous compounding, what is the answer? Round your answer to the hundredth's place.
Answer:
Show work in this space.
Click here to see answer by ankor@dixie-net.com(15657)  |
Question 83570: Write the indicated equation for each geometric solid.
1.)The surface area of a cube with an edge of x centimetres long.
I got the answer s=24x
2.)The volume of a cylinder with an height of 5 metres and a radius of x metres.
I got the answer V=≈x^2*5 ≈ is pie (3.14).
Click here to see answer by bucky(2189) |
Question 83754: A regular square pyramid is inscribed in a come with radius 4 cm. and height 4 cm.
A. What is the volume of the pyramid?
I know that the volume of the pyramid equals Lateral Area+Base, which is  P being the perimeter of the base and L being the slant height. I am not able to get beyond this point on matter how hard I try.
B. Find the slant height of the pyramid and the cone.
I have tried at this one many times but have not been able to get anything. I know that the slant height forms a triangle with the radius and the height, but I do not know where to go from there.
Please help me!
Click here to see answer by stanbon(57377) |
Question 84398: A BUILDER IS ADDING A20'X28' ROOM TO AN EXISTING HOUSE. THE FLOORING CHOICES ARE AN 8"X8" TILE THAT COST $0.98 PER TITLE ,OR A 12"X12" TITLE THAT COST $1.98 PER TITLE. APPROX HOW MUCH WILL THE BUILDER SAVE BY USING THE LESS EXPENSIVE OPTION? NEED TO KNOW HOW TO SOLVE THIS PROBLEM
Click here to see answer by checkley75(3666) |
Question 86389: ) 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 121 cubic centimeters.
a) Write h as a function of r. Keep "" in the function's equation.
Answer:
Show work in this space.
b) What is the measurement of the height if the radius of the cylinder is 3 centimeters? Round your answer to the hundredth's place.
Answer:
Show work in this space.
c) Graph this function.
Show graph here.
Click here to see answer by jim_thompson5910(28595) |
Question 87325: I have no idea what I'm doing, please help!
1. Assume you have a fire truck that has a tank that is 60"x70"x57".
A. How many gallons of water will it hold?
B. At the station, you fill the tank. You use an overhead fill that puts out 162 gallons per minute. How long will it take to fill the tank?
C. How much extra weight will it add to the truck when full?
D. If your hose puts out a maximum of 1260 gallons per minute, how long will you have to hook up a hydrant if you run at max?
E. A tanker comes to the scene that is 12 ft long and has a diameter of 6 ft. How many gallons of water will the tanker add to the scene?
A. I got 1039.05 galllons.
B. I got 6.41 minutes
C. 8,671.15 lbs
I am completely confused on D & E Please help!
Click here to see answer by ankor@dixie-net.com(15657) |
Question 90624: Please help me to solve this problem.
A cylindrical glass tube closed at one end has a radius of 5 centimeters. It is filled with Mercury up to the brim. If the mass of the metal is about 300 grams and its density id 13.7 g/cm3, what is the height of the cylinder?
Click here to see answer by scott8148(6628)  |
Question 90627: Please help me to solve this problem.
380 grams of liquid whose density id 0.95 g/cc is poured into the graduated cylinder. When 100 grams of metal is submerged into the liquid, the liquid level in the graduated cylinder rises to 450 cc. What is the density of the metal?
Click here to see answer by zerosignal(28)  |
Question 76333: A cylindrical tank with diameter 60cm and length 150cm rests on its side.
The fluid in the tank leaks from a valve that is 20cm off the ground. When
no more fluid leaks out , what is the volume of the remaining fluid?
Click here to see answer by zerosignal(28) |
Question 92690: I am really bad at solving word problems. I am not sure how to make the equation and then solve it. Please help me.
The volume of the box is represented by  Find the polynomial that represents the area of the bottom of the box.
Click here to see answer by Nate(3500) |
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