A water storage tank is shaped like a
circular cylinder with half of a sphere at each end. Find the volume of the tank if the cylindrical section is 100 cm long with a 40cm diameter. Use 3.14 for ~~ Be sure to round the final answer to two decimal places.
(Here are my choices of answers)
A. 33,493.33 cm^
B. 125,600.33cm^
C. 159,093.33cm^
D. 192,587.33cm^
( ^ symbol means 3)
I have tried to work this problem and came up with (c) 159,093.33cm^ I just
am not sure that I've worked this problem correctly.
Can someone please check to make sure that I am right?
Thank you!
Your answer is not right. It should be
pi* D^2 h /4 = 125,600, if you use 3.14 for pi, as directed.
Actually, the answer should be rounded off to two significant figures (130,000 in this case), not two figures past the decimal point.
I am surprised and a bit shocked that the teacher or textbook does not realize this.
Volume of cyclinder=pi*r^2*h
If r=20cm and h=100 cm,
then Volume=3.14*20^2*100
V=125,600
Volume of sphere=4/3*3.14*r^3
Volume=4/3*3.14*(20)^3
V=33493.33
Total Volume=125,600+33493.33
YOUR ANSWER IS CORRECT!
TV=159,093.33
Help-- I have one person telling me my
answer is wrong and another person telling me my answer is correct!
Someone please help !!
I did not read the question in its entirety and neglected add the volume of the two hemispheres. I apologize for that.
However my comments about the number of significant figures still apply. Ask the teacher why there are more significant figures in all of the answer choices than there are in the original variables.
Please check
So you are saying my answer (C) is wrong? If it's wrong, then I need help!
No, your teacher needs help. Go with what you have.
The correct answer is C. 159,093.33 cm³.
To find the volume of the water storage tank, we need to calculate the volume of the cylindrical section and the volume of the two hemispheres at each end.
1. Volume of the cylindrical section:
The formula for the volume of a cylinder is V_cylinder = π * r^2 * h, where r is the radius and h is the height.
Given that the diameter (d) is 40 cm, the radius (r) is half of the diameter, so r = 20 cm. The height (h) of the cylindrical section is given as 100 cm.
V_cylinder = 3.14 * 20^2 * 100
V_cylinder = 3.14 * 400 * 100
V_cylinder = 125,600 cm³
2. Volume of the two hemispheres:
The formula for the volume of a sphere is V_sphere = (4/3) * π * r^3, where r is the radius.
Using the same radius of 20 cm for the hemisphere, we can calculate the volume of one hemisphere and then multiply by 2 to get the total volume of both hemispheres.
V_hemisphere = (4/3) * 3.14 * 20^3
V_hemisphere = (4/3) * 3.14 * 8,000
V_hemisphere = 33,493.33 cm³
To get the total volume, we need to add the volume of the cylindrical section and the volume of the two hemispheres:
Total Volume = V_cylinder + 2 * V_hemisphere
Total Volume = 125,600 cm³ + 2 * 33,493.33 cm³
Total Volume = 125,600 cm³ + 66,986.66 cm³
Total Volume = 192,586.66 cm³
Rounded to two decimal places, the volume of the water storage tank is approximately 192,587.33 cm³, which matches option D.