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Giải bài 2 trang 111 vở thực hành Toán 8 tập 2

Cho hình chóp tam giác đều S.MNP có độ dài cạnh đáy băng 6cm, chiều cao bằng 5cm. (H.10.4)

🧜Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

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Đề bài

Cho hình chóp tam giác đều S.MNP có độ dài cạnh đáy băng 6cm, chiều cao bằng 5cm. (H.10.4) a) Tính diện tích tam giác MNP. b) Tính thể tích hình chóp S.MNP, biết \(\sqrt {27}  \approx 5,2\)

 

Phương pháp giải - Xem chi tiết

Áp dụng công thức tính diện tích xung quanh và thể tích của hình chóp tam giác đều.

Lời giải chi tiết

a) NI = 3cm, \(\Delta MNI\) vuông tại I nên theo định lí Pythagore ta có MI2 + IN2 = MN2 hay MI2 + 322 = 62, do đó MI2 = 62 – 32.

Vậy MI2 = 27. Suy ra MI = \(\sqrt {27} \) cm.

Diện tích \(\Delta MNP\) là:\({S_{MNP}} = \frac{1}{2}MI.NP = \frac{1}{2}.5,2.6 = 15,6(c{m^2})\).b) Thể tích hình chóp S.MNP là:\(V = \frac{1}{3}S.h = \frac{1}{3}.15,6.5 = 26(c{m^3})\).

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