A circular pool 10m wide in diameter has a deck 2m wid around it. What is the area of the deck?
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To find the area of the deck around the circular pool, we need to subtract the area of the pool from the area of the deck and pool combined.
1. Start by finding the radius of the pool. The diameter of the pool is given as 10m, and since the radius is half the diameter, the radius would be 10m/2 = 5m.
2. Now, calculate the area of the pool using the formula for the area of a circle: A = πr^2, where A represents the area and r is the radius. Plugging in the values, we get A = π(5m)^2 = 25π square meters.
3. To find the area of the deck, we need to add the width of the deck to the diameter of the pool: 10m + 2m (deck width) = 12m. The deck forms a circle with a diameter of 12m.
4. Calculate the radius of the deck by dividing the diameter by 2: 12m/2 = 6m.
5. Use the formula A = πr^2 to find the area of the deck. Replacing r with 6m, we have A = π(6m)^2 = 36π square meters.
6. Subtract the area of the pool from the area of the deck and pool combined to get the area of just the deck: 36π - 25π = 11π square meters.
Therefore, the area of the deck around the circular pool is 11π square meters.