Solid melted into cones: find a missing radius or height by equal volumes

This type of question, asked 2 times: 16 Sep 2025 S1, 16 Sep 2025 S2. All 2 questions below, oldest first.

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Question 1
16 Sep 2025 S1
66 $A solid hemisphere of radius 10 cm is melted into two cones of equal height. If each cone’s radius is 5 cm, what is the height of each cone?$
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Question 2
16 Sep 2025 S2
66 $A sphere is melted and recast into 8 identical cones, each with radius 3 cm and height 4 cm. What was the radius of the original sphere?$
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