Question

drag each statement to the correct location on the table. classify the shapes based on their volumes. a cone with a radius of 12 units and a height of 6 units a cylinder with a diameter of 12 units and a height of 27 units a sphere with a diameter of 12 units a cylinder with a diameter of 8 units and a height of 18 units a sphere with a radius of 9 units a cone with a diameter of 18 units and a height of 36 units 288 π 972 π

Explanation:

Step1: Recall volume formulas

Volume of cone $V_{cone}=\frac{1}{3}\pi r^{2}h$, volume of cylinder $V_{cylinder}=\pi r^{2}h$, volume of sphere $V_{sphere}=\frac{4}{3}\pi r^{3}$.

Step2: Calculate volume of cone with $r = 12$, $h = 6$

$V_{cone1}=\frac{1}{3}\pi\times12^{2}\times6=\frac{1}{3}\pi\times144\times6 = 288\pi$.

Step3: Calculate volume of cylinder with $d = 12$ (so $r = 6$), $h = 27$

$V_{cylinder1}=\pi\times6^{2}\times27=\pi\times36\times27 = 972\pi$.

Step4: Calculate volume of sphere with $d = 12$ (so $r = 6$)

$V_{sphere1}=\frac{4}{3}\pi\times6^{3}=\frac{4}{3}\pi\times216 = 288\pi$.

Step5: Calculate volume of cylinder with $d = 8$ (so $r = 4$), $h = 18$

$V_{cylinder2}=\pi\times4^{2}\times18=\pi\times16\times18 = 288\pi$.

Step6: Calculate volume of sphere with $r = 9$

$V_{sphere2}=\frac{4}{3}\pi\times9^{3}=\frac{4}{3}\pi\times729 = 972\pi$.

Step7: Calculate volume of cone with $d = 18$ (so $r = 9$), $h = 36$

$V_{cone2}=\frac{1}{3}\pi\times9^{2}\times36=\frac{1}{3}\pi\times81\times36 = 972\pi$.

Answer:

• $288\pi$: a cone with a radius of 12 units and a height of 6 units, a sphere with a diameter of 12 units, a cylinder with a diameter of 8 units and a height of 18 units
• $972\pi$: a cylinder with a diameter of 12 units and a height of 27 units, a sphere with a radius of 9 units, a cone with a diameter of 18 units and a height of 36 units