Final answer:
The volume of the conical tank is calculated using the formula V = (1/3)πr²h, with a radius of 5m and height of 8m. The correct volume, when calculated, is approximately 66.67π cubic meters. However, this does not match any of the answer choices provided exactly.
Step-by-step explanation:
The conical tank's volume can be found using the formula V = (1/3)πr²h. In this scenario, you have provided the radius (r) as 5 meters and the height (h) as 8 meters in the question. To calculate the volume, we substitute these values into the formula:
V = (1/3)π(5 m)²(8 m)
V = (1/3)π(25 m²)(8 m)
V = (1/3)π(200 m²)
V = π(200 m² / 3)
V = (200/3)π m³
V = approximately 66.67π m³
When you calculate the volume, you find that it is roughly 66.67π cubic meters, so since this is not an exact answer option, it appears there may have been a computational error either in this calculation or the choices provided. If we continue with the formula, however, we get:
V = 200π/3 m³, which simplifies to 66.67π m³.
Given the answer options listed in the question, option b) 120π cubic meters is the closest, assuming no typographical errors in the options. However, if the options are correct as provided, none of them exactly match the calculation based on the given formula and measurements.