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:
<span>radius: 14 cm, thus diameter = 2(14) = 28 cm
height: 48 cm
diagonal: 50 cm
</span>
<span>
Thus, the lateral surface of model 1 does not meets the base at right angle.
For model 2:
</span><span>radius: 6 cm, thus diameter = 2(6) = 12 cm
height: 35 cm
diagonal: 37 cm
[</span>tex]d^2+h^2=12^2+35^2 \\ \\ =144+1,225=1,369=37^2=l^2[/tex]
Thus, the lateral surface of model 2 meets the base at right angle.
For model 3:
<span>radius: 20 cm, thus, diameter = 2(20) = 40 cm
height: 40 cm
diagonal: 60 cm
</span>
Thus, the lateral surface of model 3 does not meets the base at right angle.
For model 4:
<span>radius: 24 cm, thus, diameter = 2(24) = 48 cm
height: 9 cm
diagonal: 30 cm
</span>
Thus, the lateral surface of model 3 does not meets the base at right angle.
Therefore, the <span>model in which the lateral surface meets the base at a right angle is model 2 (option b)</span>
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:
<span>radius: 14 cm, thus diameter = 2(14) = 28 cm
height: 48 cm
diagonal: 50 cm
</span>
<span>
Thus, the lateral surface of model 1 does not meets the base at right angle.
For model 2:
</span><span>radius: 6 cm, thus diameter = 2(6) = 12 cm
height: 35 cm
diagonal: 37 cm
[</span>tex]d^2+h^2=12^2+35^2 \\ \\ =144+1,225=1,369=37^2=l^2[/tex]
Thus, the lateral surface of model 2 meets the base at right angle.
For model 3:
<span>radius: 20 cm, thus, diameter = 2(20) = 40 cm
height: 40 cm
diagonal: 60 cm
</span>
Thus, the lateral surface of model 3 does not meets the base at right angle.
For model 4:
<span>radius: 24 cm, thus, diameter = 2(24) = 48 cm
height: 9 cm
diagonal: 30 cm
</span>
Thus, the lateral surface of model 3 does not meets the base at right angle.
Therefore, the <span>model in which the lateral surface meets the base at a right angle is model 2 (option b)</span>