a cylinder and a rectangular prism have the same volume and the same height the base of the prism is a square with a side length of 9 cm what is the approximate radius of the cylinder?A. 4.5 cm B. 5.1 cmC. 12.9 cm D. 25.8 cm

Answer: Option BStep-by-step explanation: The formula of the volume of a cylinder is: [tex]V=\pi r^2h[/tex] Where the radius is "r" and the height is "h". The formula of the volume of a rectangular prism is: [tex]V=Ah[/tex] Where "A" is the area of the base and "h" is the heigth. As both volumes are equal, you can write: [tex]V=V\\\pi r^2h=Ah[/tex] Find the area of the base, which is a square, with the formula: [tex]A=s^2[/tex] Where "s" is the lenght of any side of the square. [tex]A=(9cm)^2=81cm^2[/tex] Divide both sides of the equation by "h" (because the heights are equal) and solve for the radius: [tex]\frac{\pi r^2h}{h}=\frac{Ah}{h}[/tex] [tex]\pi r^2=81cm^2\\\\r=\sqrt{\frac{81cm^2}{\pi}}[/tex] [tex]r=5.07cm[/tex]≈5.1 cm