Storm sewers are hollow cylinders with outside radius of 0.9 m and inside radius of 0.7m. If a section of storm sewer is 2.5m long, what volume of concrete is needed to make it? Please help..
cross section area = pi(.9)^2 - pi(.7)^2
volume = 2.5 * pi (.81-.49)
mjcknm;dmkvfkb k b
To find the volume of the storm sewer, we need to find the difference in volume between the outer and inner cylinders.
The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the radius and h is the height.
Let's first calculate the volume of the outer cylinder:
V_outer = π * (0.9m)^2 * 2.5m
Next, let's calculate the volume of the inner cylinder:
V_inner = π * (0.7m)^2 * 2.5m
To find the volume of concrete needed, we need to subtract the volume of the inner cylinder from the volume of the outer cylinder:
Volume of concrete = V_outer - V_inner
Volume of concrete = π * (0.9m)^2 * 2.5m - π * (0.7m)^2 * 2.5m
Simplifying,
Volume of concrete = π * 0.81m^2 * 2.5m - π * 0.49m^2 * 2.5m
Volume of concrete = π * (0.81m^2 - 0.49m^2) * 2.5m
Finding the difference between the squares,
Volume of concrete = π * 0.32m^2 * 2.5m
Finally,
Volume of concrete ≈ 2.517 m^3
Therefore, approximately 2.517 cubic meters of concrete is needed to make the storm sewer.
To find the volume of concrete needed to make the storm sewer, we need to calculate the volume of the hollow cylinder.
The formula for the volume of a hollow cylinder is:
V = πh(R^2 - r^2)
Where:
V is the volume
π is a mathematical constant approximately equal to 3.14159
h is the height or length of the cylinder
R is the outside radius
r is the inside radius
Given information:
The outside radius, R = 0.9 m
The inside radius, r = 0.7 m
The length of the cylinder, h = 2.5 m
Now, let's calculate the volume:
V = πh(R^2 - r^2)
V = 3.14159 * 2.5 * (0.9^2 - 0.7^2)
V ≈ 22.21 cubic meters
Therefore, approximately 22.21 cubic meters of concrete are needed to make the storm sewer.