Problem 15 · 2025 Math Kangaroo
Hard
Geometry & Measurement
proportion
When Grandma started knitting wool socks, she had a ball of wool with a diameter of 30 cm. After she has finished knitting 70 socks, the remaining ball of wool has a diameter of 15 cm. How many more socks can Grandma knit?
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Answer: E — 10
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Hint 1 of 2
Wool used is proportional to volume, which scales with the cube of the diameter.
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Hint 2 of 2
Volumes go as 30³ : 15³ = 8 : 1, so the leftover is the same size as what 10 socks need.
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Approach: volume scales as diameter cubed
- Volumes are proportional to 30³ = 27000 and 15³ = 3375, ratio 8:1.
- 70 socks used 27000 − 3375 = 23625 units, i.e. 337.5 per sock.
- Remaining 3375 ÷ 337.5 = 10 more socks.
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