Question

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Answer 1

Answer:

b) A cylinder in which h = 3 and d = 6 has a volume of 27π in^3; therefore, Wilson is correct.

Step-by-step explanation:

$\text{The formula of a volume of a cone:}\\\\V_{cone}=\dfrac{1}{3}\pi r^2H\\\\r-radius\\H-height\\\\\text{The formula of a volume of a cylinder:}\\\\V_{cylinder}=\pi r^2H}\\\\\text{If the cylinder and the cone have the same diameter,}\\\text{then have the same radius.}\\\\diameter\ d=2r\to r=\dfrac{d}{2}\\\\d=6\ in\to r=\dfrac{6}{2}=3\ in\\\\\text{Substitute:}\\\\V_{cone}=9\pi\ in^3,\ r=3\ in:\\\\9\pi=\dfrac{1}{3}\pi(3^2)(H)\\\\9\pi=3H\pi\qquad\text{divide both sides by}\ 3\pi\\\\3=H\to H=3\ in$

$\text{Calculate the volume of a cylinder:}\\\\V_{cylinder}=\pi(3^2)(3)=27\pi\ in^3$