3. A cylindrical tin with one end open has diameter 140 mm and height 50 mm . calculate the i. Area of the base ii. Curved surface area iii. Total surface area

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Sure, let's solve each part step by step for the cylindrical tin with one end open.

**Given:**
- **Diameter (D)** = 140 mm
- **Radius (r)** = Diameter/2 = 140 mm / 2 = 70 mm
- **Height (h)** = 50 mm

---

### **i. Area of the Base**

The base of the cylinder is a circle. The area $$ A $$ of a circle is given by:
$$
A = \pi r^2
$$

**Calculation:**
$$
A = \pi \times (70 \, \text{mm})^2 = \pi \times 4900 \, \text{mm}^2 = 4900\pi \, \text{mm}^2
$$

**Approximate Value (using $$ \pi \approx 3.14 $$):**
$$
A \approx 4900 \times 3.14 = 15,\!386 \, \text{mm}^2
$$

**Answer:**
$$
\boxed{\text{i. Area of the base} = 4900\pi \, \text{mm}^2 \approx 15,\!386 \, \text{mm}^2}
$$

---

### **ii. Curved Surface Area (CSA)**

The curved surface area (also known as the lateral area) of a cylinder is calculated by:
$$
\text{CSA} = 2\pi r h
$$

**Calculation:**
$$
\text{CSA} = 2 \times \pi \times 70 \, \text{mm} \times 50 \, \text{mm} = 7000\pi \, \text{mm}^2
$$

**Approximate Value:**
$$
\text{CSA} \approx 7000 \times 3.14 = 21,\!980 \, \text{mm}^2
$$

**Answer:**
$$
\boxed{\text{ii. Curved Surface Area} = 7000\pi \, \text{mm}^2 \approx 21,\!980 \, \text{mm}^2}
$$

---

### **iii. Total Surface Area (TSA)**

Since the cylinder has one end open, the total surface area is the sum of the curved surface area and the area of the single base.

$$
\text{TSA} = \text{CSA} + \text{Area of Base} = 7000\pi + 4900\pi = 11,\!900\pi \, \text{mm}^2
$$

**Approximate Value:**
$$
\text{TSA} \approx 11,\!900 \times 3.14 = 37,\!366 \, \text{mm}^2
$$

**Answer:**
$$
\boxed{\text{iii. Total Surface Area} = 11,\!900\pi \, \text{mm}^2 \approx 37,\!366 \, \text{mm}^2}
$$

---

**Summary of Results:**
1. **Area of the base:** $$ 4900\pi \, \text{mm}^2 $$ (≈ 15,386 mm²)
2. **Curved Surface Area:** $$ 7000\pi \, \text{mm}^2 $$ (≈ 21,980 mm²)
3. **Total Surface Area:** $$ 11,\!900\pi \, \text{mm}^2 $$ (≈ 37,366 mm²)
**i. Area of the base:** $$ 4900\pi \, \text{mm}^2 $$ (≈ 15,386 mm²) **ii. Curved Surface Area:** $$ 7000\pi \, \text{mm}^2 $$ (≈ 21,980 mm²) **iii. Total Surface Area:** $$ 11,\!900\pi \, \text{mm}^2 $$ (≈ 37,366 mm²)

A cylindrical tin with one end open has diameter 140 mm and height 50 mm . calculate the
i. Area of the base
ii. Curved surface area
iii. Total surface area

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