Sketch the region enclosed by the lines x=0, x=5, y=3 and y=8. Revolve the region around the y-axis. Identify the solid formed by the revolution(1 point) Responses Cylinder Cylinder Pyramid Pyramid Sphere Sphere Cone
Cylinder
Calculate the volume of the solid described above. Round your answer to the nearest whole number(1 point)
To calculate the volume of the cylinder formed by revolving the region around the y-axis, we can use the formula for the volume of a cylinder:
V = πr^2h
where r is the radius and h is the height.
In this case, the height of the cylinder is the difference in the y-values of the lines y=8 and y=3, which is 8 - 3 = 5 units.
The radius is the distance from the y-axis to the line x=5, which is 5 units.
Plugging these values into the formula:
V = π(5^2)(5)
V = 25π(5)
V = 125π
To get the approximate volume to the nearest whole number, we can substitute π with approximately 3.14:
V ≈ 125(3.14)
V ≈ 392 cubic units
Therefore, the volume of the solid formed by revolving the region around the y-axis is approximately 392 cubic units.