To give:An example of two cylinders that have the same lateral area and different surface areas. Describe the lateral area and surface area of each.
Answer to Problem 42HP
The radii two cylinders having same lateral area but different surface areas are 4 units and 2 units and their heights are 5 units and 10 units respectively. The lateral area of first cylinder is
Explanation of Solution
Given data:
The two cylinders that have the same lateral area and different surface areas.
Concept used:
The lateral area of a cylinder of height h and radius r is given by
Calculations:
Suppose two cylinders of heights
Now let we set
The surface areas of the cylinders are
Let height and radius of one cylinder are 4 units and 5 units respectively. The lateral area of this cylinder is
The height and radius of other cylinder are 2 units and 10units respectively. The lateral area of this cylinder is
Conclusion:
The radii two cylinders having same lateral area but different surface areas are 4 units and 2 units and their heights are 5 units and 10 units respectively. The lateral area of first cylinder is
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