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A candle manufacturer sells cylindrical candles in sets of three. Each candle in the set is a different size. The smallest candle has a radius of 0.5 inches and a height of 3 inches. The other two candles are scaled versions of the smallest, with scale factors of 2 and 3. How much wax is needed to create one set of candles? in cubic inches

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W0lf93
To find out how much wax is needed for the candles we need to figure out the volume of each candle. We know radius r=0.5 inches and height h=3 inches of the smallest candle and we know that the middle candle has r2=2r=1 inch and h2=2h=6 inches and the biggest candle has r3=3r=1.5 inches and h3=3h=9 inches. So now we need the formula for volume: V=pi*r^2*h and we simply plug in the numbers. First candle is V=3.14*(0.5^2)*3=2.355 inches^3. Middle candle: V2=3.14*(1^2)*6=18.84 inches^3. Biggest candle: V3=3.14*(1.5^2)*9=63.585 inches^3. So overall wax needed to create all three candles is V+V2+V3=2.355 inches^3 + 18.84 inches^3 + 63.585 inches^3=84.78 inches^3.

Answer:

First candle is V=3.14*(0.5^2)*3=2.355 inches^3. Middle candle: V2=3.14*(1^2)*6=18.84 inches^3. Biggest candle: V3=3.14*(1.5^2)*9=63.585 inches^3. So overall wax needed to create all three candles is V+V2+V3=2.355 inches^3 + 18.84 inches^3 + 63.585 inches^3=84.78 inches^3.

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