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개념 기사 기사 작성법
내가 아는 수학개념을 쉽게 설명해주세요!
[개념 기사] 캔은 왜 원기둥일까?
Dr.K 2021.04.25 19:14

캔이 왜 원기둥인지 알아봅시다. 캔의 역사를 알기 위해서는 먼 시간여행을 떠나야 합니다.

 

1810년 겨울, 어느 한 상인이 병조림을 시켜 먹으려고 합니다. 하지만 날씨가 너무 추워서인지 그냥 먹기에는 어려웠습니다. 그래서 자기가 가지고 있는 작은 철판에 음식을 부어서 데워 먹었죠. 바로 그때 이 상인은 아이디어가 번쩍 떠올랐습니다. 바로 통조림을 만드는 것은 어떨까? 라고 말이죠. 이 특허품은 영국의 왕 조지 3세로 부터 특허를 받았습니다. 캔의 역사가 막 시작 되는 것이죠.

이 상인 피터 듀란드 입니다.

 

그런데 우리가 알고 싶은 것은 캔이 왜 원기둥일까? 라는 점이죠. 자, 우리가 캔을 만드는 회사의 직원이라고 할 때 가장 비용을 줄이는 방법은 없는지, 가장 경제적인 소비를 할 수 있을지를 고민을 해보아야 합니다. 이때 필요한 것은 캔의 겉넓이 입니다. 모양이 다를 때 부피는 같아도 겉넓이는 다를 수 있습니다.

 

그럼 겉넓이를 구하고 싶으면 어떻게 해야 할까요? 각각의 면의 넓이를 다 더하면 됩니다.

여기 원기둥이 있습니다. 원기둥의 전개도를 펼쳤을 때,PPT - 8. 입체도형의 성질 PowerPoint Presentation, free download - ID:3435219

원이 두개가 나오고 직사각형 한개가 나옵니다. 이때는 두 원과 직사각형을 더하면 됩니다. 원의 반지름을 r이라고 하면 밑면의 넓이는 πr²이 두개 있으므로 2πr², 직사각형은 가로×세로 인데 여기서 가로는 밑면인 원에 둘레와 같습니다.

 

또한 높이를 h라고 놓으면 원의 둘레는 2πrh 이므로 2πr²+2πrh 가 겉넓이 구하는 공식이 나오게 되는 것이죠.

 

 

그럼, 정삼각기둥, 정사각기둥 원기둥이 높이가 다 같고 부피도 같은 조건이라면(높이를 10cm 부피를 1000cm³) 정삼각기둥의 겉넓이는 (밑넓이)×2+(옆넓이)이고  AD=10 DE=EF=FD'=A"B=A"C=15.2 밑면△ABC에서 높이는 13.16이므로 ½×15.2×13.16×2+45.6×10=200.032+456=656.032(cm²)

 

 

정사각기둥(정육면체)의 겉넓이는 모든 모서리는 10cm이므로 10×10×2+40×10=200+400=600(cm²)

 

 

이제, 주인공인 원기둥의 겉넓이는   반지름이 5.644이고 높이가 10이므로 3.14×5.644²×2+35.44×10=200.048+354.4=554.4(cm²)

즉, 높이가 같고 부피가 같다는 조건에서 겉넓이는 원기둥이 가장 작기 때문에 원기둥을 사용한답니다. 원기둥은 컵이나 통, 휴지 심에도 원기둥이 녹아 들어가 있습니다. 한번 일상생활에서 원기둥인 사례를 찾아보세요.

 

 

 

 

 

퀴즈, 수학자들이 가장 좋아하는 보석은 무엇일까요? 넌센스 입니다.(파이가 들어감)

 

 

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