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Cone recast into another cone: new height or volume left over

This type of question, asked 2 times: 19 Sep 2025 S2, 26 Sep 2025 S3. All 2 questions below, oldest first.

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  1. Question 1

    19 Sep 2025 S2

    63
    A cone has height h and radius r. The cone is melted and recast into a smaller cone whose height is h2\frac{h}{2} and radius isr3\frac{r}{3} What fraction of the original volume is unused?

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  2. Question 2

    26 Sep 2025 S3

    64
    A cone is melted and recast into another cone with half the radius. Find the new height if the original height was 12 cm.

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