Ta có:

• Đường kính bóng: \(6,4 \textrm{ } \text{cm} \Rightarrow r = 3,2 \textrm{ } \text{cm}\)
• Hộp trụ chứa vừa khít 3 bóng theo chiều dọc ⇒
• • Bán kính trụ: \(R = 3,2 \textrm{ } \text{cm}\)
  • Chiều cao trụ: \(h = 3 \times 6,4 = 19,2 \textrm{ } \text{cm}\)

a) Thể tích hộp (hình trụ)

\(V_{\text{tr}ụ} = \pi R^{2} h = 3,14 \cdot \left(\right. 3,2 \left.\right)^{2} \cdot 19,2\) \(= 3,14 \cdot 10,24 \cdot 19,2 = 617,56 \textrm{ } \text{cm}^{3}\)

👉 Làm tròn: 618 cm³

b) Thể tích phần không bị chiếm bởi 3 quả bóng

Thể tích 1 quả bóng:

\(V_{\text{c} \overset{ˋ}{\hat{\text{a}}} \text{u}} = \frac{4}{3} \pi r^{3} = \frac{4}{3} \cdot 3,14 \cdot \left(\right. 3,2 \left.\right)^{3}\) \(= \frac{4}{3} \cdot 3,14 \cdot 32,768 = 137,26 \textrm{ } \text{cm}^{3}\)

3 quả:

\(V_{3 \text{c} \overset{ˋ}{\hat{\text{a}}} \text{u}} = 3 \cdot 137,26 = 411,78 \textrm{ } \text{cm}^{3}\)

Phần thể tích còn lại:

\(V_{\text{tr} \overset{ˊ}{\hat{\text{o}}} \text{ng}} = 617,56 - 411,78 = 205,78 \textrm{ } \text{cm}^{3}\)

1. Đầu đinh: hình trụ
2. • Đường kính: \(8 \textrm{ } \text{mm} \Rightarrow r = 4 \textrm{ } \text{mm}\)
   • Chiều cao: \(2 \textrm{ } \text{mm}\)

\(V_{1} = \pi r^{2} h = 3,14 \cdot 4^{2} \cdot 2 = 100,48 \textrm{ } \text{mm}^{3}\)

1. Thân đinh: hình trụ
2. • Đường kính: \(4 \textrm{ } \text{mm} \Rightarrow r = 2 \textrm{ } \text{mm}\)
   • Chiều dài: \(25 \textrm{ } \text{mm}\)

\(V_{2} = 3,14 \cdot 2^{2} \cdot 25 = 314 \textrm{ } \text{mm}^{3}\)

1. Mũi đinh: hình nón
2. • Bán kính: \(2 \textrm{ } \text{mm}\)
   • Chiều cao: \(5 \textrm{ } \text{mm}\)

\(V_{3} = \frac{1}{3} \pi r^{2} h = \frac{1}{3} \cdot 3,14 \cdot 2^{2} \cdot 5 = 20,93 \textrm{ } \text{mm}^{3}\)

Tổng thể tích 1 chiếc đinh:

\(V = 100,48 + 314 + 20,93 = 435,41 \textrm{ } \text{mm}^{3}\)

10 chiếc đinh:

\(V_{10} = 435,41 \cdot 10 = 4354,1 \textrm{ } \text{mm}^{3}\)

Đổi ra ml:

\(1 \textrm{ } \text{ml} = 1000 \textrm{ } \text{mm}^{3} \Rightarrow V = 4,3541 \textrm{ } \text{ml}\)

Ta có:

• Ly hình trụ: đường kính đáy \(6 \textrm{ } \text{cm} \Rightarrow r = 3 \textrm{ } \text{cm}\)
• Bóng bàn: đường kính \(40 \textrm{ } \text{mm} = 4 \textrm{ } \text{cm} \Rightarrow R = 2 \textrm{ } \text{cm}\)

a) Thể tích quả bóng bàn

Quả bóng là hình cầu:

\(V = \frac{4}{3} \pi R^{3} = \frac{4}{3} \cdot 3,14 \cdot 2^{3}\) \(V = \frac{4}{3} \cdot 3,14 \cdot 8 = 33,49 \textrm{ } \text{cm}^{3}\)

👉 Thể tích quả bóng ≈ 33,49 cm³

b) Thể tích phần nổi của quả bóng

Thể tích phần nước dâng lên trong ly:

\(V_{\text{d} \hat{\text{a}} \text{ng}} = S_{đ \overset{ˊ}{\text{a}} \text{y}} \cdot h = \pi r^{2} \cdot h = 3,14 \cdot 3^{2} \cdot 7,2\) \(V_{\text{d} \hat{\text{a}} \text{ng}} = 3,14 \cdot 9 \cdot 7,2 = 203,47 \textrm{ } \text{cm}^{3}\)

Nhưng Nam chỉ rót 200 cm³ nước, nên phần chênh lệch là thể tích phần chìm của quả bóng:

\(V_{\text{ch} \overset{ˋ}{\imath} \text{m}} = 203,47 - 200 = 3,47 \textrm{ } \text{cm}^{3}\)

Thể tích phần nổi:

\(V_{\text{n}ổ\text{i}} = V_{\text{c} \overset{ˋ}{\hat{\text{a}}} \text{u}} - V_{\text{ch} \overset{ˋ}{\imath} \text{m}} = 33,49 - 3,47 = 30,02 \textrm{ } \text{cm}^{3}\)

I love living in the city for many reasons. Firstly, I love the diversity of cuisine and culture, where I can easily find delicious food and experience many different entertainment activities. Secondly, the city offers many job and study opportunities, helping me develop my career and personal knowledge. Thirdly, moving around the city is quite convenient thanks to the developed public transportation system, although sometimes I still encounter traffic congestion. In short, despite certain limitations, I still enjoy the dynamism, convenience and opportunities that urban life brings.

I love living in the city for many reasons. Firstly, I love the diversity of cuisine and culture, where I can easily find delicious food and experience many different entertainment activities. Secondly, the city offers many job and study opportunities, helping me develop my career and personal knowledge. Thirdly, moving around the city is quite convenient thanks to the developed public transportation system, although sometimes I still encounter traffic congestion. In short, despite certain limitations, I still enjoy the dynamism, convenience and opportunities that urban life brings.

I love living in the city for many reasons. Firstly, I love the diversity of cuisine and culture, where I can easily find delicious food and experience many different entertainment activities. Secondly, the city offers many job and study opportunities, helping me develop my career and personal knowledge. Thirdly, moving around the city is quite convenient thanks to the developed public transportation system, although sometimes I still encounter traffic congestion. In short, despite certain limitations, I still enjoy the dynamism, convenience and opportunities that urban life brings.

I love living in the city for many reasons. Firstly, I love the diversity of cuisine and culture, where I can easily find delicious food and experience many different entertainment activities. Secondly, the city offers many job and study opportunities, helping me develop my career and personal knowledge. Thirdly, moving around the city is quite convenient thanks to the developed public transportation system, although sometimes I still encounter traffic congestion. In short, despite certain limitations, I still enjoy the dynamism, convenience and opportunities that urban life brings.

I love living in the city for many reasons. Firstly, I love the diversity of cuisine and culture, where I can easily find delicious food and experience many different entertainment activities. Secondly, the city offers many job and study opportunities, helping me develop my career and personal knowledge. Thirdly, moving around the city is quite convenient thanks to the developed public transportation system, although sometimes I still encounter traffic congestion. In short, despite certain limitations, I still enjoy the dynamism, convenience and opportunities that urban life brings.

I love living in the city for many reasons. Firstly, I love the diversity of cuisine and culture, where I can easily find delicious food and experience many different entertainment activities. Secondly, the city offers many job and study opportunities, helping me develop my career and personal knowledge. Thirdly, moving around the city is quite convenient thanks to the developed public transportation system, although sometimes I still encounter traffic congestion. In short, despite certain limitations, I still enjoy the dynamism, convenience and opportunities that urban life brings.

I love living in the city for many reasons. Firstly, I love the diversity of cuisine and culture, where I can easily find delicious food and experience many different entertainment activities. Secondly, the city offers many job and study opportunities, helping me develop my career and personal knowledge. Thirdly, moving around the city is quite convenient thanks to the developed public transportation system, although sometimes I still encounter traffic congestion. In short, despite certain limitations, I still enjoy the dynamism, convenience and opportunities that urban life brings.