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Giải bài tập 14 trang 99 SGK Toán 9 tập 2 - Chân trời sáng tạo

Ta coi một ống nghiệm có phần trên là hình trụ và phần dưới là hình cầu (Hình 4). Hãy tính thể tích nước cần để đổ đầy vào ống nghiệm, coi bề dày của ống nghiệm không đáng kể.

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

Toán - Văn - Anh
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Đề bài

Ta coi một ống nghiệm có phần trên là hình trụ và phần dưới là hình cầu (Hình 4). Hãy tính thể tích nước cần để đổ đầy vào ống nghiệm, coi bề dày của ống nghiệm không đáng kể.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

-  Dựa vào công thức thể tích của hình trụ: V = S.h =\(\pi \)r2h

-  Dựa vào công thức thể tích của hình cầu có bán kính R là: V = \(\frac{4}{3}\pi {R^3}\).

Lời giải chi tiết

Bán kính phần hình trụ là: \(R = \frac{d}{2} = \frac{2}{2} = 1\) cm Thể tích phần hình trụ là: 

Vtrụ =\(\pi \)r2h = \(\pi {.1^2}.8 \approx 25\)(cm3).

Thể tích hình cầu là:

Vcầu = \(\frac{4}{3}\pi {R^3} = \frac{4}{3}\pi .{(4,25)^3} \approx 322\)(cm3).

Thể tích nước cần để đổ đầy bình là:

V = Vtrụ + Vcầu \( \approx \) 25 + 322 = 347(cm3).

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