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Giải bài 5.27 trang 35 sách bài tập toán 12 - Kết nối tri thức

Một quả bóng hình cầu có bán kính 2 m được treo lơ lửng trên một mặt đất phẳng. Tâm quả bóng cách mặt đất 10 m. Chọn hệ trục tọa độ Oxyz có gốc tọa độ O là hình chiếu vuông góc của tâm quả cầu trên mặt đất, tia Oz chứa tâm của quả cầu, các trục Ox, Oy thuộc mặt đất như hình vẽ.

🔯Tổng hợp đề thi học kì 2 lớp 12 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Hoá - Sinh - Sử - Địa
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Đề bài

Một quả bóng hình cầu có bán kính 2 m được treo lơ lửng trên một mặt đất phẳng. Tâm quả bóng cách mặt đất 10 m. Chọn hệ trục tọa độ Oxyz có gốc tọa độ O là hình chiếu vuông góc của tâm quả cầu trên mặt đất, tia Oz chứa tâm của quả cầu, các trục Ox, Oy thuộc mặt đất như hình vẽ.

Phương pháp giải - Xem chi tiết

Xác định tâm mặt cầu dựa trên giả thiết tâm thuộc trục Oz và cách mặt đất 10 m.

Lời giải chi tiết

Do tâm quả bóng thuộc tia Oz và cách mặt đất 10 m nên quả cầu có tâm \(I\left( {0;0;10} \right)\). Bán kính quả bóng bằng 2, do đó ta có phương trình của mặt cầu bề mặt quả bóng là \({x^2} + {y^2} + {\left( {z - 10} \right)^2} = 4\).

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