A right circular cylinder has a height of 18 | vedclass

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(B) The total surface area $(TSA)$ of the original cylinder is given by $2 \pi r(r + h)$.Substituting the values: $TSA_{original} = 2 	imes \frac{22}

Vedclass · Accepted Answer

$56$

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(B) The total surface area $(TSA)$ of the original cylinder is given by $2 \pi r(r + h)$.Substituting the values: $TSA_{original} = 2 	imes \frac{22}{7} 	imes 7 	imes (7 + 18) = 44 	imes 25 = 1100 \, cm^2$.When the cylinder is cut into $3$ equal parts by $2$ cuts parallel to the base,each new cylinder has a height of $h' = \frac{18}{3} = 6 \, cm$ and the same radius $r = 7 \, cm$.The $TSA$ of one smaller cylinder is $2 \pi r(r + h') = 2 	imes \frac{22}{7} 	imes 7 	imes (7 + 6) = 44 	imes 13 = 572 \, cm^2$.The total surface area of the $3$ smaller cylinders is $3 	imes 572 = 1716 \, cm^2$.The increase in surface area is $1716 - 1100 = 616 \, cm^2$.The percentage increase is $\frac{616}{1100} 	imes 100 = 56 \%$.

$A$ right circular cylinder has a height of $18 \, cm$ and a radius of $7 \, cm$. The cylinder is cut into three equal parts by $2$ cuts parallel to the base. What is the percentage increase in the total surface area (in $\%$)?

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