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개념 기사 기사 작성법
내가 아는 수학개념을 쉽게 설명해주세요!
[개념 기사] 아이스크림 콘에 숨은 수학의 원리?!
집돌이 페렐만 2020.05.27 05:16

(대표 이미지 및 이하 모든 이미지 출처 : PIXABAY) 

어느 더운 여름날, 철수와 영희가 길을 걷고 있습니다. 

해는 쨍쨍 비치는데 물은 없고, 목은 타들어가는데... 

그때 이들을 반기는 것은 아이스크림 가게! 

안녕하세요, 박성현 기자입니다. 5월인데도 더운 날씨에 다들 고생을 하고 계실 텐데요. 이렇게 더운 날씨에는 역시 아이스크림이죠! 

음, 그런데 아이스크림의 콘은 왜 원뿔 모양일까요?

 

 

[처음에는 콘이 없었다?] 

여러분, 아이스크림은 얼마나 오래된 음식일까요? 50년? 100년? 

놀랍게도 이미 5000년 전부터 중국인들은 눈에 과일즙을 섞어 만들어 먹었습니다! 우리나라에서도 이미 삼국시대 이전부터 얼음을 사용한 것으로 추정되고, 신라 제3대 왕인 유리왕 때부터 이미 얼음을 저장해 사용했다고 합니다. 

현대적인 아이스크림의 형태가 정착된 것은 18세기 영국이라고 합니다. 이전까지는 눈이나 얼음을 사용했지만, 1718년 한 요리책에서 처음 우유를 사용해 지금의 아이스크림이 탄생했습니다. 

그런데 그때까지도 아이스크림에 콘은 없었다고 합니다. 콘은 언제 생긴 것일까요? 

콘은 1904년, 미주리 주에서 열린 엑스포에서 탄생했습니다. 원래 당시에는 아이스크림을 종이 등에 싸서 팔았습니다. 그런데 아이스크림을 포장할 종이가 부족해진 아이스크림 가게의 상인이 마침 옆에 있던 와플 가게에서 와플을 사서 대신 쓴 것이 아이스크림 콘의 시초입니다!

 

 

[그런데 왜 하필 원뿔 모양일까?] 

그런데 왜 와플을 원뿔 모양으로 접어서 사용했을까요? 

철수와 영희의 대화에서 답을 찾을 수 있습니다. 

철수 : 우리 팔팔콘 사자! 그런데 돈이 없어서 1개밖에 못 사겠네... 

영희 : 그러면 우리 둘이 나눠서 먹으면 되지! 음... 나는 배부르니까 윗부분만 먹을게. 나머지는 네가 다 먹어! 

철수 : 정말? 앗싸! 

10분 뒤 

철수 : 이상하네. 분명 넌 6분의 1 지점까지만 먹고 나머지는 다 내가 먹었는데 왜 얼마 안 먹은 것 같지?

 

도대체 어떻게 된 일일까요? 

밑면의 반지름이 4cm이고 높이가 10cm인 원뿔이 있다고 가정해봅시다. 그리고 반지름이 4cm인 반구도 상상해봅시다.

원뿔의 부피는 \frac{1}{3}    imes(높이)×(밑면의 넓이) 입니다.

구의 부피는 \frac{4}{3} \pi(반지름)^{3}입니다.

왜 이런 공식이 나올까요?

원기둥에 내접하는 구와 원뿔의 부피의 비는 원기둥 : 구 : 원뿔 = 3 : 2 : 1입니다.

따라서 원뿔의 부피는 원기둥의 부피인 높이 x 밑면의 넓이에 3분의 1을 곱한 값이 됩니다.

구는 어떨까요? 원기둥의 밑면의 반지름은 구의 반지름과 같고, 원기둥의 높이는 구의 반지름의 2배이므로 이를 이용해 원기둥의 부피를 나타내면 2 x 반지름 x 반지름×π = 2 × (반지름)^{^{3}} x π가 됩니다. 그런데 구의 부피는 원기둥의 부피는 원기둥의 ⅔이므로 \frac{4}{3} \pi(반지름)^{3}이라는 공식이 나오게 되는 것입니다!

이때 반지름을 r, 높이는 h라고 하면 구의 부피 공식은 \frac{4}{3}\pi r^{3}이 됩니다.

따라서 위의 원뿔의 부피는 \frac{160}{3}\picm^{^{3}} 이고, 반구의 부피는 \frac{128}{3}\pi cm^{3}입니다. 차이가 얼마 안나지요?

 

이처럼 원뿔 모양으로 아이스크림 콘을 만들면 윗부분이 많으니 양도 더 많아 보이고, 먹음직스러워 보입니다. 또한 콘을 잡는 밑 부분은 윗부분에 비해 면적이 좁아 손의 열이 적게 전달되니 아이스크림도 느리게 녹습니다. 

또 다른 이유도 있습니다. 

만약 원기둥 모양으로 콘을 만들어 넣는다면, 밖으로 나오는 부분을 제외하면 콘 안에 들어갈 아이스크림의 양이 원뿔 모양 콘의 3배나 됩니다. 부피의 비가 3 : 1이니까요. 

만약 구 모양으로 콘을 만든다면 세우기가 어려울 거예요. 그렇지만 원뿔 모양 콘은 삼각형과 같이 안정적으로 서 있을 수 있답니다.

 

아이스크림 콘에 숨은 수학적 원리를 알겠나요? 전 철수에게 콘의 비밀을 알려주러 가야겠네요~!

[오늘의 퀴즈]

우리 주변에는 아이스크림 콘처럼 원뿔 모양인 물건이 많습니다. 고깔 모자나 크리스마스 트리가 그 예입니다.

여러분도 주변의 원뿔을 찾고 왜 원뿔 모양인지 생각해보세요~

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수학동아 기자의 한마디
수학동아 기자 2020.05.28
아이스크림 콘과 함께 돌아온 집돌이 페렐만 기자의 글, 잘 읽었습니다.
일상에서 쉽게 찾을 수 있는 주제로, 이미지 출처도 잊지 않고 글 쓰는 자세를 항상 칭찬합니다:)

우리가 아는 아이스크림 콘은 구와 원뿔의 부피 차이, 모양 차이 때문에 지금까지 이어져 온 것 같네요!
글 중간에 구의 부피와 원뿔의 부피 비가 2:1인데 원뿔과 반구의 부피값이 각각 160π/3, 128π/3이 나왔어요? 실수가 있는지 다시 살펴보길 바라요.

기사를 읽을수록 아이스크림이 생각나네요. 여러분은 어떤 맛 아이스크림을 좋아하나요? 저는 초코칩이 콕콕 박힌 초콜릿 콘을 좋아해요!
이 기사 어떠셨나요?

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  •  
    집돌이 페렐만 Lv.9 2020.05.30 02:54

    ㅋㅋ 저도 기사 다 쓰고 아이스크림을 먹었다는 여담이...

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