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A 33m tall tank in the shape of an inverted right circular cone has a volume of 1659

cubic meters.
1. Find the diameter of the tank
2. If the radius and height of the tank are both scaled up by 25%, what is the new
volume of the tank?

1 Answer

3 votes

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)

User Themagicalyang
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