Math Problem Statement

Solar​ (photovoltaic) cells convert sunlight directly into electricity. If solar cells were​ 100% efficient, they would generate about 1000 watts of power per square meter of surface area when exposed to direct sunlight. With lower​ efficiency, they generate proportionally less power. For​ example, 10% efficient cells generate 100 watts of power in direct sunlight. Suppose you want to supply 1 kilowattnothing of power to a house by putting solar panels on its roof. For solar cells with the average power of 46 watts per square meter of solar​ panels, how many square meters of solar panels would you​ need? Assume you can make use of the average power from the solar cells​ (by, for​ example, storing energy in batteries until it is​ needed). How many square meters of solar pannels would you need?

Solution

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Math Problem Analysis

Mathematical Concepts

Ratio and Proportion
Unit Conversion

Formulas

Area (A) = Total Power Needed / Power per Square Meter
A = 1000 watts / 46 watts per square meter

Theorems

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Suitable Grade Level

Grades 9-11