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Giải bài tập 10.9 trang 105 SGK Toán 9 tập 2 - Kết nối tri thức

Một quả bóng đá có chu vi của đường tròn lớn bằng 68,5cm. Quả bóng được ghép nối bởi các miếng da hình lục giác đều màu trắng và đen, mỗi miếng có diện tích bằng (49,83c{m^2}). Hỏi cần ít nhất bao nhiêu miếng da để làm quả bóng trên? (Coi phần mép khâu không đáng kể).

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
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Đề bài

Một quả bóng đá có chu vi của đường tròn lớn bằng 68,5cm. Quả bóng được ghép nối bởi các miếng da hình lục giác đều màu trắng và đen, mỗi miếng có diện tích bằng \(49,83c{m^2}\). Hỏi cần ít nhất bao nhiêu miếng da để làm quả bóng trên? (Coi phần mép khâu không đáng kể).

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

+ Tính bán kính đường tròn lớn, nó bằng bán kính mặt quả bóng đá. + Tính diện tích mặt quả bóng đá bán kính R: \(S = 4\pi {R^2}\). + Số miếng da ít nhất cần bằng: \(\frac{S}{{49,83}}\).

Lời giải chi tiết

Bán kính đường tròn lớn chính là bán kính quả bóng. Bán kính quả bóng là: \(R = 68,5:\pi :2 = \frac{{137}}{{4\pi }}\left( {cm} \right)\) Diện tích mặt quả bóng là: \(S = 4\pi {R^2} = 4\pi .{\left( {\frac{{137}}{{4\pi }}} \right)^2} = \frac{{18\;769}}{{4\pi }}\left( {c{m^2}} \right)\) Số miếng da cần dùng là: \(\frac{{18\;769}}{{4\pi }}:49,83 \approx 29,97\) (miếng) Vậy cần ít nhất 30 miếng da để làm quả bóng trên.

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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