The model in which the lateral surface meets the base at right angle is : Model 1.
<h3>What is a lateral surface?</h3>
The lateral surface of an object is all surfaces of that object excluding its base and top.
Analysis:
To know the exact model, we check for the models in which their dimensions form a Pythagorean triplet otherwise a right-angled triangle.
For Pythagorean triplet, the square of the diagonal must be equal to the sum of squares of the other two sides.
Model 1
Diagonal = 50cm, radius = 14cm, lateral height = 48cm
= 
+ 
2500 = 196 + 2304
2500 = 2500. Forms Pythagorean triplet
Model 2
Diagonal= 37cm, radius = 6cm lateral height = 35cm
= 
+ 
1369 = 1225 +36
1369 
1261
Model 3
Diagonal = 60cm, radius = 20cm lateral height = 40cm
= 
+ 
3600 = 400 + 1600
3600 2000
Model 4
Diagonal = 30cm, radius = 24cm, lateral height = 9cm
= 
+ 
900 = 576 + 81
900 657
Therefore the lateral surface model 1 meets the base at right angle
In conclusion, the lateral surface of model 1 meets the base at right angles as the dimensions form a right-angled triangle.
Learn more about Pythagorean triplet: brainly.com/question/20894813
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