Cone and hemisphere with the same base and equal volumes: height of the cone

The same question, asked 2 times: 13 Sep 2025 S3, 16 Sep 2025 S1. Every wording below, oldest first.

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Question 1
13 Sep 2025 S3
70 $A cone and a hemisphere have the same volume and base radius. Find the ratio of the height of the cone to its radius.$
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Question 2
16 Sep 2025 S1
65 $A hemisphere and a cone share the same base and have equal volumes. Given that their common radius is R, determine the height of the cone.$
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