Javier has four cylindrical models. the heights, radii, and diagonals of the vertical cross-sections of the models are shown in the table. model 1 radius: 14 cm height: 48 cm diagonal: 50 cm model 2 radius: 6 cm height: 35 cm diagonal: 37 cm model 3 radius: 20 cm height: 40 cm diagonal: 60 cm model 4 radius: 24 cm height: 9 cm diagonal: 30 cm in which model does the lateral surface meet the base at a right angle? a. model 1 b. model 2 c. model 3 d. model 4

Given the heights, radii, and diagonals of the vertical cross-sections of the models, the model in which the lateral surface meet the base at a right angle is the model in which the height, the diameter and the diagonal of the vertical cross-section forms a right triangle.

i.e. the sum of the squares of the height (h) and the diameter (d) gives the square of the diagonal vertical cross-section (l).

For model 1:

radius: 14 cm, thus diameter = 2(14) = 28 cm
height: 48 cm
diagonal: 50 cm



Thus, the lateral surface of model 1 does not meets the base at right angle.

For model 2:

radius: 6 cm, thus diameter = 2(6) = 12 cm
height: 35 cm
diagonal: 37 cm



Thus, the lateral surface of model 2 meets the base at right angle.

For model 3:

radius: 20 cm, thus, diameter = 2(20) = 40 cm
height: 40 cm
diagonal: 60 cm



Thus, the lateral surface of model 3 does not meets the base at right angle.

For model 4:

radius: 24 cm, thus, diameter = 2(24) = 48 cm
height: 9 cm
diagonal: 30 cm



Thus, the lateral surface of model 3 does not meets the base at right angle.

Therefore, the model in which the lateral surface meets the base at a right angle is model 2 (option b)

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