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Giải bài tập 9.20 trang 86 SGK Toán 9 tập 2 - Cùng khám phá

Một bình nước dạng hình trụ kết hợp với nửa hình cầu có kích thước như Hình 9.54. Khi bình nước nằm ngang, mực nước trong bình cao 20 cm. a) Tính thể tích nước trong bình. b) Nếu đặt bình nước thẳng đứng sao cho phần nửa hình cầu ở trên thì chiều cao mực nước trong bình là bao nhiêu?

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

Toán - Văn - Anh
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Đề bài

ܫMột bình nước dạng hình trụ kết hợp với nửa hình cầu có kích thước như Hình 9.54. Khi bình nước nằm ngang, mực nước trong bình cao 20 cm.

a) Tính thể tích nước trong bình.

𒅌b) Nếu đặt bình nước thẳng đứng sao cho phần nửa hình cầu ở trên thì chiều cao mực nước trong bình là bao nhiêu?

 

Phương pháp giải - Xem chi tiết

Thể tích của hình cầu là: \(V = \frac{4}{3}\pi {R^3}\)(với R là bán kính hình cầu)

Diện tích mặt cầu là: S = \(4\pi {R^2}\)

Diện tích hình tròn là: S = \(\pi {R^2}\)

Lời giải chi tiết

a) Thể tích bình là:

\(V = \frac{1}{2}\frac{4}{3}\pi {.20^3} + \pi {.20^2}.60 = \frac{{88000}}{3}\pi \) (cm3)

Vì chiều cao mực nước trong bể bằng nửa chiều cao bể nên thể tích nước trong bình bằng một nửa thể tích bể. Thể tích nước trong bể là:

\(V = \frac{1}{2}.\frac{{88000}}{3}\pi  = \frac{{44000}}{3}\pi \) (cm3)

b) Ta có Vnước < Vtrụ

Suy ra khi dựng thẳng đứng bình thì chiều cao của nước < chiều cao của hình trụ hay Vnước = \(\pi {.20^2}\). hnước = \(\frac{{44000}}{3}\pi \) (cm3)

Suy ra hnước🍌 = \(\frac{{44000}}{3}\pi : \left(\pi {.20^2}\right) = \frac{{110}}{3}\) cm.

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