A rubber cylinder R of length L and cross-sectional area A is compressed inside a steel cylinder by a force F that applies a uniformly distributed pressure to the rubber (see figure).
(a) Derive a formula for the lateral pressure between the rubber and the steel. (Disregard friction between the rubber and the steel, and assume that the steel cylinder is rigid when compared to the rubber.)
(b) Derive a formula for the shortening d of the rubber cylinder.

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