Geometric Measurement and Dimension: Informal Arguments for Circle and Solid Formulas (CCSS.G-GMD.1)

Use $V=\pi r^2 h=\pi\cdot 3^2\cdot 8=72\pi$. Choice C uses $2\pi r$ instead of $r^2$, and D forgets to square $r$.

Use $V=\tfrac{1}{3}\pi r^2 h=\tfrac{1}{3}\pi\cdot 5^2\cdot 6=50\pi$. Choice B forgets the $\tfrac{1}{3}$; A uses $2\pi r$ in place of $r^2$.

Use $V=\tfrac{4}{3}\pi r^3=\tfrac{4}{3}\pi\cdot 4^3=\tfrac{256}{3}\pi$. Choice B omits the $\tfrac{4}{3}$; C forgets to divide by 3.

Use $V=\pi r^2 h=\pi\cdot 7^2\cdot 2=98\pi$. Choice A uses $2\pi r$; B forgets to square $r$.

Use $V=\tfrac{1}{3}\pi r^2 h=\tfrac{1}{3}\pi\cdot 2^2\cdot 9=12\pi$. Choice A forgets the $\tfrac{1}{3}$; C forgets to square $r$.

Use $V=\pi r^2 h$. Substitute $r=5$, $h=9$: $V=\pi(5)^2(9)=\pi(25)(9)=225\pi$. $90\pi$ uses $2\pi r h$ (circumference times height), $45\pi$ forgets to square $r$, and $235\pi$ is an arithmetic slip.

Use $V=\tfrac{1}{3}\pi r^2 h$. Substitute $r=4$, $h=6$: $V=\tfrac{1}{3}\pi(4)^2(6)=\tfrac{1}{3}\pi(16)(6)=32\pi$. $96\pi$ forgets the $\tfrac{1}{3}$, $48\pi$ uses $2\pi r h$, and $8\pi$ forgets to square $r$.

Use $V=\tfrac{4}{3}\pi r^3$. Substitute $r=6$: $V=\tfrac{4}{3}\pi(6)^3=\tfrac{4}{3}\pi(216)=288\pi$. $216\pi$ uses $\pi r^3$ (missing $\tfrac{4}{3}$), $144\pi$ is surface area $4\pi r^2$, and $48\pi$ uses $\tfrac{4}{3}\pi r^2$ (forgot the cube).

Use $V=\pi r^2 h$. Substitute $r=3$, $h=10$: $V=\pi(3)^2(10)=\pi(9)(10)=90\pi$. $60\pi$ uses $2\pi r h$, $30\pi$ forgets to square $r$, and $80\pi$ is an arithmetic slip.

Use $V=\tfrac{1}{3}\pi r^2 h$. Substitute $r=5$, $h=9$: $V=\tfrac{1}{3}\pi(5)^2(9)=\tfrac{1}{3}\pi(25)(9)=\tfrac{225}{3}\pi=75\pi$. $225\pi$ uses the cylinder formula (forgot $\tfrac{1}{3}$), $90\pi$ uses $2\pi r h$, and $15\pi$ forgets to square $r$.