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Giải bài tập 9.13 trang 83 SGK Toán 9 tập 2 - Cùng khám phá

Một chiếc cốc hình trụ có phần đáy bên trong là một hình tròn bán kính bằng 12 cm. Chiều cao của mực nước trong cốc là 10 cm (Hình 9.48). a) Tính thể tích nước trong cốc. b) Thả một quả cầu bằng kim loại có bán kính 4 cm vào cốc cho đến khi quả cầu chìm hẳn xuống đáy cốc và mực nước đứng yên. Hỏi mực nước trong cốc tăng thêm bao nhiêu centimet?

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

Toán - Văn - Anh
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Đề bài

Một chiếc cốc hình trụ có phần đáy bên trong là🧸 một hình tròn bán kính bằng 12 cm. Chiều cao của mực nước trong cốc là 10 cm (Hình 9.48).

a) Tính thể tích nước trong cốc.

b) Thả một quả cầu bằng kim loại có bán kí𒁏nh 4 cm vào cốc cho đến khi quả cầu chìm hẳn xuốꦬng đáy cốc và mực nước đứng yên. Hỏi mực nước trong cốc tăng thêm bao nhiêu centimet?

Phương pháp giải - Xem chi tiết

Thể tích của hình trụ: \(V = \pi {R^2}h\) (với R là bán kính đáy hình trụ, h là chiều cao)

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

Lời giải chi tiết

a) Thể tích nước trong cốc hình trụ là:

\(V = \pi {R^2}h = \pi {.12^2}.10 = 1440\pi\)cm3

b) Thể tích quả cầu kim loại là:

\(V = \frac{4}{3}\pi {R^3} = \frac{4}{3}\pi {.4^3} = \frac{256}{3}\pi\) cm3

Thể tích nước sau khi thả quả cầu là:

\( 1440\pi + \frac{256}{3}\pi = \frac{4576}{3}\pi\) cm3

Chiều cao mực nước khi đó là: \(\frac{4576}{3} \pi: (\pi.12^2) \approx 10,6\) cm Mực nước trong cốc tăng lên là: 10,6 – 10 = 0,6 cm. Vậy mực nước trong cốc tăng lên khoảng 0,6 cm.

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