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(B) The total surface area $(TSA)$ of a cylinder is given by $2 \pi r h + 2 \pi r^2 = 231 \, cm^2$.Given that the curved surface area $(CSA)$ is $(2/3

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$269.5$

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(B) The total surface area $(TSA)$ of a cylinder is given by $2 \pi r h + 2 \pi r^2 = 231 \, cm^2$.Given that the curved surface area $(CSA)$ is $(2/3)$ of the total surface area:$CSA = 2 \pi r h = (2/3) 	imes 231 = 154 \, cm^2$.Since $TSA = CSA + 2 \pi r^2$,we have $231 = 154 + 2 \pi r^2$,which implies $2 \pi r^2 = 77 \, cm^2$.Thus,$\pi r^2 = 77/2 = 38.5 \, cm^2$.Using $\pi = 22/7$,we get $(22/7) 	imes r^2 = 38.5$,so $r^2 = (38.5 	imes 7) / 22 = 12.25$.Therefore,$r = \sqrt{12.25} = 3.5 \, cm$ (or $7/2 \, cm$).Now,substitute $r$ into the $CSA$ formula: $2 	imes (22/7) 	imes (7/2) 	imes h = 154$.$22 	imes h = 154$,so $h = 154 / 22 = 7 \, cm$.The volume of the cylinder is $V = \pi r^2 h = (22/7) 	imes (7/2) 	imes (7/2) 	imes 7 = 269.5 \, cm^3$.

$A$ solid cylinder has a total surface area of $231 \, cm^2$. Its curved surface area is $(2/3)$ of the total surface area. Find the volume of the cylinder (in $cm^3$).

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