A solid cylinder has a total surface area of | vedclass

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(C) Let the height of the cylinder be $h \, cm$ and the radius of the base be $r \, cm$.According to the question,the total surface area is $2 \pi r^2

Vedclass · Accepted Answer

$539$

Vedclass · Answer

(C) Let the height of the cylinder be $h \, cm$ and the radius of the base be $r \, cm$.According to the question,the total surface area is $2 \pi r^2 + 2 \pi r h = 462 \, cm^2 \dots (1)$.The curved surface area is given as $\frac{1}{3}$ of the total surface area:Curved surface area $= 2 \pi r h = \frac{1}{3} 	imes 462 = 154 \, cm^2$.Substituting this into equation $(1)$:$2 \pi r^2 + 154 = 462$$2 \pi r^2 = 462 - 154 = 308$$2 	imes \frac{22}{7} 	imes r^2 = 308$$r^2 = \frac{308 	imes 7}{44} = 7 	imes 7 = 49$$r = 7 \, cm$.Now,using $2 \pi r h = 154$:$2 	imes \frac{22}{7} 	imes 7 	imes h = 154$$44 	imes h = 154$$h = \frac{154}{44} = 3.5 \, cm$ (or $\frac{7}{2} \, cm$).The volume of the cylinder is $V = \pi r^2 h = \frac{22}{7} 	imes 7 	imes 7 	imes 3.5 = 22 	imes 7 	imes 3.5 = 539 \, cm^3$.

$A$ solid cylinder has a total surface area of $462 \, cm^2$. Its curved surface area is $\frac{1}{3}$ of its total surface area. The volume of the cylinder is.......$cm^3$.

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