Question

the cone and cylinder shown below have congruent bases and equal heights. complete the following. (a) volume of the cone: m³ (b) volume of the cylinder: m³ (c) volume of the cone = × volume of the cylinder this equation is true for all cylinders and cones. this equation is true for all cylinders and cones with congruent bases and equal heights. this equation is true only for the cylinder and cone shown above.

Explanation:

Step1: Recall volume formulas

The volume formula for a cone is $V_{cone}=\frac{1}{3}Bh$, and for a cylinder is $V_{cylinder}=Bh$, where $B$ is the base - area and $h$ is the height. Given $B = 18m^{2}$ and $h = 3m$.

Step2: Calculate volume of the cone

$V_{cone}=\frac{1}{3}\times B\times h=\frac{1}{3}\times18\times3$
$V_{cone}=18m^{3}$

Step3: Calculate volume of the cylinder

$V_{cylinder}=B\times h = 18\times3$
$V_{cylinder}=54m^{3}$

Step4: Find the ratio

$\frac{V_{cone}}{V_{cylinder}}=\frac{18}{54}=\frac{1}{3}$, so $V_{cone}=\frac{1}{3}V_{cylinder}$. This relationship is true for all cylinders and cones with congruent bases and equal heights.

Answer:

(a) $18$
(b) $54$
(c) $\frac{1}{3}$; This equation is true for all cylinders and cones with congruent bases and equal heights.