Question

$\large{ \underline{ \tt{ \purple{Question :}}}}$

The diameters of two cones are equal. If their slant heights are in the ratio 5 : 4, find the ratio of their curved surfaces.​

Answer 1

The diameters of two cones are equal. If their slant heights are in the ratio 5 : 4, find the ratio of their curved surfaces.

Answer 5:4

Answer 2

Given : The Diameter of two cones are equal .If their Slant heights are in the ratio 5:4

To Find : Find the Ratio of Curved Surface Area

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SolutioN :

$\dag \; {\underline{\underline{\pmb{\sf{ Here \; we \; Have \; :- }}}}}$

• 1st Slant Height = 5y
• 2nd Slant Height = 4y
• $\sf{ r_1 = \dfrac{d_1}{2} }$

• $\sf{ r_2 = \dfrac{d_2}{2} }$

$\dag \; {\underline{\underline{\pmb{\sf{ Calculating \; the \; Ratio \; :- }}}}}$

$\begin{gathered} \; \; \; \red\longmapsto \; \; {\purple{\pmb{\sf { Ratio = \dfrac{ \pi \times r \times l }{ \pi \times r \times l } }}}} \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \longmapsto \; \; \sf { Ratio = \dfrac{ \pi \times \bigg\lgroup \dfrac{d_1}{2} \bigg\rgroup \times l }{ \pi \times \bigg\lgroup \dfrac{d_2}{2} \bigg\rgroup \times l } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \longmapsto \; \; \sf { Ratio = \dfrac{ \pi \times \bigg\lgroup \dfrac{d_1}{2} \bigg\rgroup \times 5y }{ \pi \times \bigg\lgroup \dfrac{d_2}{2} \bigg\rgroup \times 4y } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \longmapsto \; \; \sf { Ratio = \dfrac{ \pi \times \bigg\lgroup \cancel{\dfrac{d_1}{2}} \bigg\rgroup \times 5y }{ \pi \times \bigg\lgroup \cancel{\dfrac{d_2}{2}} \bigg\rgroup \times 4y } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \longmapsto \; \; \sf { Ratio = \dfrac{ \pi \times 5y }{ \pi \times 4y } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \longmapsto \; \; \sf { Ratio = \dfrac{ \pi \times 5 \times y }{ \pi \times 4 \times y } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \longmapsto \; \; \sf { Ratio = \dfrac{ \pi \times 5 \times \cancel{y} }{ \pi \times 4 \times \cancel{y} } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \longmapsto \; \; \sf { Ratio = \dfrac{ \cancel{\pi} \times 5 }{ \cancel{\pi} \times 4 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \longmapsto \; \; \sf { Ratio = \dfrac{ 5 }{ 4 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \; \; \; \longmapsto \; \; {\underline{\boxed{\pmb{\pink{\frak{ Ratio = 5:4 }}}}}} \; \bigstar \\ \\ \\ \end{gathered}$

$\therefore \;$ Ratio of the Surface Area is 5:4 .

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