Please help me!! i really don't know how to do it. can someone show me how to do it.
A propane gas tank consists of a cylinder with a hemisphere at each end. Find the volume of the tank if the overall length is 20 feet and the diameter of the cylinder is 6 feet (round to an exact number) (see figure in the website below).
www.webassign.net/userimages/2.png?db=v4net&id=454246
length = 20 = cylinder length + 2 R = L + 6
so L = 14 feet
volume = sphere volume + cylinder volume
= (4/3) pi (3)^3 + pi (3)^2 * 14
= 36 pi + 126 pi
@Reiny and @Damon thanks, so my answer is 36 pi + 126 pi = 508.94
yes
thanks guys
To find the volume of the tank, we'll need to break it down into two parts: the cylinder and the two hemispheres.
First, let's calculate the volume of the cylinder:
The formula for the volume of a cylinder is V_cylinder = π * r^2 * h, where r is the radius of the cylinder and h is the height of the cylinder.
In this case, the diameter of the cylinder is given as 6 feet, so the radius (r) would be half of that, which is 3 feet.
To find the height (h) of the cylinder, we know that the overall length of the tank is 20 feet. Since the total length includes both hemispheres, the length of the cylinder would be 20 feet - 2(radius of hemisphere).
The radius of the hemisphere is half the diameter, so it will be 3 feet as well.
Therefore, the height (h) of the cylinder is 20 feet - 2 * 3 feet = 20 feet - 6 feet = 14 feet.
Now we can calculate the volume of the cylinder using the formula V_cylinder = π * r^2 * h, so the volume of the cylinder is V_cylinder = π * 3 feet^2 * 14 feet.
Next, let's calculate the volume of the hemispheres:
The formula for the volume of a hemisphere is V_hemisphere = (2/3) * π * r^3.
In this case, since the radius is 3 feet, the volume of each hemisphere would be: V_hemisphere = (2/3) * π * 3 feet^3.
Since there are two hemispheres, the total volume of the hemispheres would be twice that value, so V_hemispheres = 2 * (2/3) * π * 3 feet^3.
Now, add the volume of the cylinder and the volume of the hemispheres to get the overall volume of the tank: V_tank = V_cylinder + V_hemispheres.
To find the final answer, take the value of V_tank and express it using π, but round it to an exact number, as mentioned in the question.
The two hemispheres make one whole sphere of radius 3, so
its volume = (4/3)π(27) = 36π ft^3
the cylinder part also has a radius of 3 and a length 14 , (20 - 2 radii)
so its volume = π(9)(14) = ..... ft^3
add them up