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Question about Volume and Area: Cylinder

Source: ENEM


Mathematics

Volume and Area: Cylinder

Medium

(ENEM 2020) - Question Medium of Mathematics

a.
b.
c.
d.
e.

Answer sheet

1st step: Identify the given information: - Both water tanks have the same volume. - The height of the type B water tank is equal to 25% of the height of the type A water tank. 2nd step: Establish variables for the information: - Volume of the type A water tank: V_A - Volume of the type B water tank: V_B - Height of the type A water tank: h_A - Height of the type B water tank: h_B = 0.25 * h_A - Radius of the type A water tank: R - Radius of the type B water tank: r_B (the value we want to find) 3rd step: Write the formula for the volume of a cylinder: Volume = π * (radius^2) * height 4th step: Write the equation for the volume of water tanks A and B: V_A = π * (R^2) * h_A V_B = π * (r_B^2) * h_B 5th step: Since V_A = V_B, we can equate the two equations: π * (R^2) * h_A = π * (r_B^2) * h_B 6th step: Use the relationship between the heights of water tanks A and B: h_B = 0.25 * h_A. Substitute in the equation above: π * (R^2) * h_A = π * (r_B^2) * (0.25 * h_A) 7th step: Simplify the equation by canceling common terms: R^2 = r_B^2 * 0.25 8th step: Multiply both sides of the equation by 4 to isolate r_B^2: 4 * R^2 = r_B^2 9th step: Calculate the square root of both sides of the equation to find r_B: r_B = 2 * R Therefore, the radius of the type B water tank is equal to "2 * R", which is the correct answer among the provided alternatives.

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