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Sagot :
We are given that 12 cones contain 203.5 cubic inches. Since there a re 12, the volume of each individual cone is:
[tex]V=\frac{203.5in^3}{12}=16.96in^3[/tex]Now, the volume of a cone is given by the following formula:
[tex]V=\frac{1}{3}\pi r^2h[/tex]Where "r" is the radius and "h" the height. Solving for the radius first by multiplying by 3:
[tex]3V=\pi r^2h[/tex]Now we divide both sides by pi:
[tex]\frac{3V}{\pi}=r^2h[/tex]Now we divide both sides by "h":
[tex]\frac{3V}{\pi h}=r^2[/tex]Now we take the square root to both sides:
[tex]\sqrt[]{\frac{3V}{\pi h}}=r[/tex]Now we replace the known values:
[tex]\sqrt[]{\frac{3\mleft(16.96in^3\mright)}{\mleft(3.14\mright)\mleft(5in\mright)}}=r[/tex]Solving the operations:
[tex]\sqrt[]{\frac{50.88in^2}{15.7}}=r[/tex][tex]\sqrt[]{3.2in^2}=r[/tex][tex]1.8in=r[/tex]Therefore, the radius is 1.8 inches.
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