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Giải bài 4 trang 116 vở thực hành Toán 8 tập 2

Người ta làm mô hình kim tự tháp ở cổng vào của bảo tàng Louvre. Mô hình có dạng hình chóp tứ giác đều, chiều cao 21 m, độ dài cạnh đáy là 34 m

Tổng hợp đề thi học kì 2 lớp 8 tất c♏ả các môn - Kết nối tri thức

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

Người ta làm mô hình kim tự tháp ở cổng vào của bảo tàng Louvre. Mô hình có dạng hình chóp tứ giác đều, chiều cao 21 m, độ dài cạnh đáy là 34 m a) Tính thể tích hình chóp  b) Tính tổng diện tích các tấm kính để phủ kín bốn mặt bên hình chóp này, biết rằng người ta đo được độ dài cạnh bên của hình chóp là 31, 92m.

Phương pháp giải - Xem chi tiết

- Áp dụng công thức tính thể tích hình chóp.

- Tổng diện tích các tấm kính để phủ kín bốn mặt bên hình chóp là diện tích xung quanh của hình chóp.

Lời giải chi tiết

Hình 10.18 minh họa cho bài toán như sau.

a) Thể tích hình chóp tứ giác đều là:$V=\frac{1}{3}{{S}_{day}}.h=\frac{1}{3}{{.34}^{2}}.21=8092\left( c{{m}^{3}} \right)$b) CI = 17m.Áp dụng định lí Pythagore cho tam giác SCI vuông tại I, ta có:

CI2 + SI2 = SC2

172 + SI2 = 31,922

SI2 = 729,89

SI = 27,02Diện tích xung quanh của hình chóp tứ giác đều là:\({{S}_{xq}}=pd\approx \frac{34.4}{2}.27,02=1837,36\left( {{m}^{2}} \right)\).

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