Answer:
A) the diameter of the tank is approximately 7.74 meters.
B) the new volume of the tank, when the radius and height are scaled up by 25%, is approximately 1897 cubic meters.
Explanation:
Given:
Volume of the tank = 1659 cubic meters
Height of the tank (h) = 33 meters
We can rearrange the formula to solve for the radius (r):
V = (1/3) * π * r^2 * h
1659 = (1/3) * π * r^2 * 33
r^2 = (1659 * 3) / (33 * π)
r^2 ≈ 15
r ≈ √15
r ≈ 3.87 meters
The diameter of the tank is twice the radius:
Diameter = 2 * r
Diameter ≈ 2 * 3.87
Diameter ≈ 7.74 meters
Given:
Original radius (r) ≈ 3.87 meters
Original height (h) = 33 meters
Calculating the new dimensions:
New radius (r') ≈ 3.87 + 0.25 * 3.87
New height (h') ≈ 33 + 0.25 * 33
New volume (V') can be calculated using the formula for the volume of a cone:
V' = (1/3) * π * (r')^2 * (h')
Substituting the new dimensions into the formula:
V' = (1/3) * π * [(3.87 + 0.25 * 3.87)^2] * [(33 + 0.25 * 33)]
Calculating the new volume:
V' ≈ 1897 cubic meters (rounded to the nearest cubic meter)