Math, asked by safiyafathima728, 4 months ago

A slant height of a furstom of a cone is 4cm and perimeter of its circular bases are 18cm and 6cm. find the curved surface area of a furstom of a cone

Answers

Answered by SachinGupta01
9

 \bf \:  \underline{Given} :

 \sf \implies The \:  slant \:  height  \: of \:  a  \: furstom  \: of \:  a  \: cone = 4 \:  cm.

 \sf \implies Perimeter  \: of  \: circular \:  bases = 18  \: cm  \: and  \: 6 \:  cm.

 \bf \: \underline{ To \:  find} :

 \sf \implies Curved  \: surface \:  area \:  of \:  furstom \:  of  \: a  \: cone.

 \bf \:  \underline{Formula  \: to \:  be \:  used},

 \implies \boxed{ \red{ \sf \: CSA  \: of  \: cone = \pi (r_1 + r_2)l }}

 \sf \: Where,

 \sf \implies \underline{r_1 = 18\: cm} \:   \: , \: \:  \underline{r_2 = 6\: cm}\: \:,  \:   \:  \underline{l= \: 4 cm}

 \sf \underline{Finding\: the\:value\:of\:  r_1}

 \sf \: Circumference \:  of \:  1^{st}  \: circular \:  base = 18 \:  cm

 \implies \sf \sf 2 \pi r_1 = 18

 \implies \sf \sf  r_1 =  \dfrac{18}{2 \pi}

 \red{ \implies \sf \sf  r_1 =  \dfrac{9}{\pi} }

 \sf \underline{Finding\: the\:value\:of\:  r_2}

 \sf \: Circumference \:  of \:  2^{nd}  \: circular \:  base = 6 \:  cm

 \implies \sf \sf 2 \pi r_2 =6

 \implies \sf \sf  r_2 =  \dfrac{6}{2 \pi}

 \red{ \implies \sf \sf  r_2 =  \dfrac{3}{\pi} }

 \sf  \underline{Now, we  \: will  \: find \:  the  \: curved  \: surface  \: area.}

 \sf \implies  Curved  \: surface  \: area =  \: \pi  \times l(r_1 + r_2)

 \sf \implies  \pi  \times 4 \bigg( \dfrac{9}{\pi}+  \dfrac{3}{\pi}\bigg)

 \sf \implies  \pi  \times 4   \:  \bigg( \dfrac{12}{\pi} \bigg)

 \sf \implies   4 \pi   \:  \bigg( \dfrac{12}{\pi} \bigg)

 \sf \implies   4 \!\!\!\not\pi   \:  \bigg( \dfrac{12}{\not{\pi}} \bigg)

 \sf \implies   4 \times 12

 \red{ \sf \implies   48 \: cm^{2}}

 \underline{ \boxed{  \pink{\sf Hence, curved  \: surface \:  area  \: of \:  a  \: frustom  \: of  \: a  \: cone = 48  \: cm^{2} }}}

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