Respuesta :
[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=1.5\\ h=5 \end{cases}\implies V=\cfrac{\pi (1.5)^2(5)}{3}\implies V=\cfrac{11.25\pi }{3} \\\\\\ V= 3.75\pi \implies V\approx 11.78~cm^3\qquad \leftarrow \textit{for one candle} \\\\\\ \stackrel{\textit{how many times does 11.78 go into 301.59?}}{301.59\div 11.78\implies 26}\qquad \leftarrow \textit{rounded up}[/tex]
The volume of the cone is one-third of the product of its base area and its height. The maximum number of candles that can be made from the liquid wax is 25.
What is the volume of a cone?
The volume of the cone is one-third of the product of its base area and its height. It is given by the formula,
The Volume of Cone = (1/3) × π × (d/2)² × h
The volume of wax that is needed to make a single candle with a diameter of 3 cm and height of 5 cm is,
The Volume of Cone = (1/3) × π × (d/2)² × h
The Volume of Candle = (1/3) × π × (3/2)² × 5 = 11.78 cm³
The total wax available is 301.59 cm³, while the amount of wax needed to make a candle is 11.78 cm³, therefore, the number of candles that can be made with the total wax is,
The Number of candles = (301.59 cm³/ 11.78 cm³) = 25.5999
Since a half candle can not be produced, therefore, the maximum number of candles that can be made from the liquid wax is 25.
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