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2.1.1. Explain the term Radus. (2) 2.1.2. Calculate the radius of the water tank, (2) 2.1.3. The lid of the water tank most be painted on the outside for it to be valible. Calculate the art of the lid (in \( \left.\mathrm{m}^{2}\right) \) ) the diameteris 28 m . (3) The following formuta may be used: Area of a circle \( =n \times(\text { radfus })^{2} \), wing \( n=3,142 \) 2.1. A one-fter tin of paint covert an area of \( 15 \mathrm{~m}^{2} \). Caiculate the sle of the area that can be covered with 17 Itres of paint. (2) 2.1.5. The laside of the tank must be sealed with waterproof paint. The lid does not get waterproofed on the inside. Calculate the interior surface area (in \( \mathrm{m}^{2} \) ) by using the following formula. Inside area \( =(2 \times \pi \times r \times h)+\left(\pi \times r^{2}\right) \), using \( \pi=3,142 \)

Ask by Fitzgerald Bryant. in South Africa
Mar 11,2025

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Answer

**2.1.1. Radius** The radius is the distance from the center of a circle to any point on its edge. It's half of the diameter. **2.1.2. Radius of the Water Tank** Given the diameter is 28 meters, the radius is: \[ \text{Radius} = \frac{28}{2} = 14 \text{ meters} \] **2.1.3. Area of the Lid** Using the formula for the area of a circle: \[ \text{Area} = 3.142 \times (14)^2 = 3.142 \times 196 \approx 615.832 \, \text{m}^2 \] **2.1.4. Area Covered by Paint** One liter covers \( 15 \, \text{m}^2 \). Therefore, 17 liters cover: \[ 17 \times 15 = 255 \, \text{m}^2 \] **2.1.5. Interior Surface Area of the Tank** The formula is: \[ A = 2 \times \pi \times r \times h + \pi \times r^2 \] However, the height \( h \) of the tank is not provided. Please supply the height to calculate the interior surface area.

Solution

Let's break down the problem step by step. ### 2.1.1. Explain the term Radius. The radius is defined as the distance from the center of a circle (or sphere) to any point on its circumference (or surface). It is half of the diameter, which is the distance across the circle through its center. ### 2.1.2. Calculate the radius of the water tank. Given that the diameter of the water tank is 28 m, we can calculate the radius \( r \) using the formula: \[ r = \frac{\text{diameter}}{2} \] Substituting the given diameter: \[ r = \frac{28}{2} = 14 \text{ m} \] ### 2.1.3. Calculate the area of the lid. The area \( A \) of a circle can be calculated using the formula: \[ A = n \times r^2 \] where \( n = 3.142 \) and \( r = 14 \text{ m} \). Now, substituting the values: \[ A = 3.142 \times (14)^2 \] Calculating \( (14)^2 \): \[ (14)^2 = 196 \] Now substituting back: \[ A = 3.142 \times 196 \] Let's calculate this area. Calculate the value by following steps: - step0: Calculate: \(3.142\times 196\) - step1: Multiply the numbers: \(615.832\) The area of the lid is approximately \( 615.832 \, \text{m}^2 \). ### 2.1.4. Calculate the size of the area that can be covered with 17 liters of paint. Given that one liter of paint covers an area of \( 15 \, \text{m}^2 \), we can calculate the total area covered by \( 17 \) liters of paint as follows: \[ \text{Total Area} = \text{Area covered by 1 liter} \times \text{Number of liters} \] Substituting the values: \[ \text{Total Area} = 15 \, \text{m}^2 \times 17 \] Let's calculate this area. Calculate the value by following steps: - step0: Calculate: \(15\times 17\) - step1: Multiply the numbers: \(255\) The total area that can be covered with 17 liters of paint is \( 255 \, \text{m}^2 \). ### 2.1.5. Calculate the interior surface area of the tank. The interior surface area \( A \) can be calculated using the formula: \[ A = (2 \times \pi \times r \times h) + (\pi \times r^2) \] However, we need the height \( h \) of the tank to proceed with this calculation. Since the height is not provided in the problem, please provide the height of the tank so we can continue with the calculation.

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The Deep Dive

To kick things off, the term "radius" refers to the distance from the center of a circle or sphere to its outer edge. It’s half of the diameter, which is the straight line that passes through the center, connecting two points on the perimeter. Understanding the radius is key when dealing with anything circular, from wheels to pizza slices! Now, diving into the real-world application: Think about how this calculation impacts various real-life scenarios! For example, knowing the radius of a water tank helps in determining the amount of water it can hold, which is crucial for a range of industries—like agriculture and manufacturing. Plus, when you're throwing a party, knowing the dimensions helps in making that perfect punch bowl!

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