Final answer:
To find the volume inside the storage tank, we add the volume of the cylinder (144π m³) to the volume of the hemisphere ((128/3)π m³), giving a total volume of approximately 538 m³ to the nearest cubic meter.
Step-by-step explanation:
The question presents a storage tank with a cylindrical shape and a hemispherical top. To find the total volume inside the storage tank, we need to calculate the volume of both the cylinder and the hemisphere separately and then add the two volumes together. The diameter of the cylinder is given as 8 meters, making the radius 4 meters (since radius is half of the diameter). The total height of the tank is 13 meters, and since this includes the hemisphere, the height of the cylindrical part is 13 meters minus the radius of the hemisphere (which is the same as the radius of the cylinder), meaning the height of the cylinder is 9 meters.
Volume of the Cylinder (Vcyl)
Vcyl = πr²h = π(4 m)²(9 m) = 144π m³
Volume of the Hemisphere (Vhemi)
Vhemi = (2/3)πr³ = (2/3)π(4 m)³ = (128/3)π m³
Total Volume
To find the total volume, we add the volumes of the cylinder and hemisphere:
Total Volume = Vcyl + Vhemi = 144π m³ + (128/3)π m³ = (512/3)π m³
To the nearest cubic meter, we calculate this using π ≈ 3.14159 and arrive at approximately 538 m³ as the total volume inside the storage tank.