If the total surface area of a cone is 3696 , | vedclass

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(C) The total surface area $(TSA)$ of a cone is given by the formula: $TSA = \pi r(r + l) = \pi rl + \pi r^{2}$.Given,$TSA = 3696 \, cm^{2}$ and the c

Vedclass · Accepted Answer

$3:5$

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(C) The total surface area $(TSA)$ of a cone is given by the formula: $TSA = \pi r(r + l) = \pi rl + \pi r^{2}$.Given,$TSA = 3696 \, cm^{2}$ and the curved surface area $(CSA)$ is $\pi rl = 2310 \, cm^{2}$.Substituting the value of $CSA$ into the $TSA$ formula:$3696 = 2310 + \pi r^{2}$.$\pi r^{2} = 3696 - 2310 = 1386$.Using $\pi = \frac{22}{7}$,we get $\frac{22}{7} r^{2} = 1386$.$r^{2} = \frac{1386 	imes 7}{22} = 63 	imes 7 = 441$.$r = \sqrt{441} = 21 \, cm$.Now,use the $CSA$ formula to find the slant height $(l)$:$2310 = \pi rl = \frac{22}{7} 	imes 21 	imes l$.$2310 = 22 	imes 3 	imes l = 66l$.$l = \frac{2310}{66} = 35 \, cm$.The ratio of the radius $(r)$ to the slant height $(l)$ is $r:l = 21:35$.Dividing both by $7$,we get $3:5$.

If the total surface area of a cone is $3696 \, cm^{2}$ and the curved surface area of a cone is $2310 \, cm^{2}$,find the ratio of the radius to the slant height.

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