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>
![d^2+h^2=28^2+48^2 \\ \\ =784+2,304=3,090\neq50^2=l^2](https://tex.z-dn.net/?f=d%5E2%2Bh%5E2%3D28%5E2%2B48%5E2%20%5C%5C%20%20%5C%5C%20%3D784%2B2%2C304%3D3%2C090%5Cneq50%5E2%3Dl%5E2)
<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>
![d^2+h^2=40^2+40^2 \\ \\ =1,600+1,600=3,200\neq60^2=l^2](https://tex.z-dn.net/?f=d%5E2%2Bh%5E2%3D40%5E2%2B40%5E2%20%5C%5C%20%5C%5C%20%3D1%2C600%2B1%2C600%3D3%2C200%5Cneq60%5E2%3Dl%5E2)
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>
![d^2+h^2=48^2+9^2 \\ \\ =2,304+81=2,385\neq30^2=l^2](https://tex.z-dn.net/?f=d%5E2%2Bh%5E2%3D48%5E2%2B9%5E2%20%5C%5C%20%5C%5C%20%3D2%2C304%2B81%3D2%2C385%5Cneq30%5E2%3Dl%5E2)
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>