A cylindrical water tank in construction has a diameter of 4 meters and a height of 6 meters. Calculate the surface area required for painting the tank excluding the top.

Question

UpStudy AI · Accepted Answer

To calculate the surface area required for painting the cylindrical water tank excluding the top, we need to find the lateral surface area and the area of the bottom base of the cylinder.

### Step 1: Identify the dimensions
- Diameter of the cylinder, $$ d = 4 $$ meters
- Radius of the cylinder, $$ r = \frac{d}{2} = \frac{4}{2} = 2 $$ meters
- Height of the cylinder, $$ h = 6 $$ meters

### Step 2: Calculate the lateral surface area
The lateral surface area $$ A_L $$ of a cylinder is given by the formula:
$$
A_L = 2 \pi r h
$$

### Step 3: Calculate the area of the bottom base
The area $$ A_B $$ of the bottom base of the cylinder is given by the formula:
$$
A_B = \pi r^2
$$

### Step 4: Total surface area for painting
The total surface area $$ A_T $$ required for painting the tank (excluding the top) is the sum of the lateral surface area and the area of the bottom base:
$$
A_T = A_L + A_B
$$

Now, let's calculate these areas step by step.

1. Calculate the lateral surface area $$ A_L $$:
   $$
   A_L = 2 \pi (2) (6)
   $$

2. Calculate the area of the bottom base $$ A_B $$:
   $$
   A_B = \pi (2)^2
   $$

3. Finally, calculate the total surface area $$ A_T $$:
   $$
   A_T = A_L + A_B
   $$

Let's perform these calculations.
Calculate the value by following steps:
- step0: Calculate:
  $$2\pi \times 2\times 6$$
- step1: Multiply the terms:
  $$24\pi $$
Calculate or simplify the expression $$ \pi * (2)^2 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\pi \times 2^{2}$$
- step1: Evaluate the power:
  $$\pi \times 4$$
- step2: Multiply:
  $$4\pi $$
Calculate or simplify the expression $$ 24 + 4 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$24+4$$
- step1: Add the numbers:
  $$28$$
### Step 5: Perform the calculations

1. **Lateral Surface Area $$ A_L $$**:
   $$
   A_L = 2 \pi (2) (6) = 24\pi \approx 75.40 \text{ square meters}
   $$

2. **Area of the Bottom Base $$ A_B $$**:
   $$
   A_B = \pi (2)^2 = 4\pi \approx 12.57 \text{ square meters}
   $$

3. **Total Surface Area $$ A_T $$**:
   $$
   A_T = A_L + A_B = 24\pi + 4\pi = 28\pi \approx 87.96 \text{ square meters}
   $$

### Final Answer
The surface area required for painting the cylindrical water tank, excluding the top, is approximately **87.96 square meters**.
The surface area required for painting the tank, excluding the top, is approximately 87.96 square meters.

A cylindrical water tank in construction has a diameter of 4 meters and a height of 6 meters. Calculate the surface area required for painting the tank excluding the top.

Upstudy AI Solution

Answer

Solution

Step 1: Identify the dimensions

Step 2: Calculate the lateral surface area

Step 3: Calculate the area of the bottom base

Step 4: Total surface area for painting

Step 5: Perform the calculations

Final Answer

Beyond the Answer

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