Larry manufactures circular garden ponds that are 1.4 feet deep and have a diameter of 12 feet. They are made out of synthetic rubber liners which she buys in rolls at a cost of $3.80 per square foot. What does the rubber cost Larry to manufacture each pond? (Use pi = 3.14 and round your final answer only.)
Question
Larry manufactures circular garden ponds that are 1.4 feet deep and have a diameter of 12 feet. They are made out of synthetic rubber liners which she buys in rolls at a cost of $3.80 per square foot. What does the rubber cost Larry to manufacture each pond? (Use pi = 3.14 and round your final answer only.)
Solution
To find the cost of the rubber for each pond, we first need to calculate the surface area of the pond. The pond is in the shape of a cylinder, so we use the formula for the surface area of a cylinder, which is 2πr(h + r). Here, r is the radius and h is the height (or depth in this case).
Step 1: Convert the diameter to radius. The radius is half of the diameter, so r = 12/2 = 6 feet.
Step 2: Substitute the values into the formula. The depth (h) is 1.4 feet and the radius (r) is 6 feet. So, the surface area = 2 * 3.14 * 6 * (1.4 + 6) = 2 * 3.14 * 6 * 7.4 = 175.84 square feet.
Step 3: Calculate the cost of the rubber. The cost of the rubber is 668.19.
So, the rubber costs Larry approximately $668.19 to manufacture each pond.
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