Question

find the ratio of curved surface area of cone if the diameter of base and equal and the Slate height or in a ratio 4:3​

Answer 1

Answer:

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• Diameter of two cones are equal
• The Ratio of their slant heights is 4:3
• Ratio of their CSA?

$\displaystyle\underline{\bigstar\:\textsf{According to the given Question :}}$

• We are given that the diameters are equal which means d¹ = d² so then their Radius will be

$\displaystyle\sf\dag \: Radius = \dfrac{D}{2}$

• Similarly the the Ratio of the slant heights are 4:3

$\displaystyle\sf \dag \: \dfrac{l_1}{l_2} = \dfrac{4}{3}$

$\displaystyle\underline{\bigstar\:\textsf{Ratio of their CSA :}}$

$\displaystyle\sf \dashrightarrow \dfrac{CSA_1}{CSA_2} = \dfrac{\pi r_1l_1}{\pi r_2l_2}$

$\sf \dashrightarrow \dfrac{CSA_1}{CSA_2} = \dfrac{\pi \times\frac{D}{2}\times 4}{\pi \times\frac{D}{2}\times 3}$

$\displaystyle\sf \dashrightarrow \dfrac{CSA_1}{CSA_2} = \dfrac{4}{3}$

$\displaystyle\sf \dashrightarrow CSA_1 : CSA_2 = 4:3$

$\displaystyle\therefore\:\underline{\textsf{The Ratio of their sides will be \textbf{ 4:3 }}}$

Answer 2

$\bigstar\huge\bf{\underline{\underline{\purple{question:}}}}$

find the ratio of curved surface area of cone if the diameter of base and equal and the Slate height or in a ratio 4:3

$\bigstar\huge\bf{\underline{\underline{\purple{given:}}}}$

Diameter of two cones are equal

The Ratio of their slant heights is 4:3

$\bigstar\huge\bf{\underline{\underline{\purple{find:}}}}$

Ratio of their CSA?

$\displaystyle\underline{\bigstar\:\textsf{ \pink According \pink to \pink the \pink given \pink Question :}}$

$\bf \large\ d¹ = d²$

$\bf \: \sf\dag \: Radius = \dfrac{D}{2}$

$\bf \ ratio \dag \ = 4 \ratio3$

$\displaystyle\sf \dag \: \dfrac{l_1}{l_2} = \dfrac{4}{3}†$

$\bf{\underline{\underline{\purple{ \underline{\bigstar\:\textsf{Ratio of their CSA :}} </p><p> \: :}}}} </p><p></p><p>$

$\begin{gathered}\displaystyle\sf \dashrightarrow \dfrac{CSA_1}{CSA_2} = \dfrac{\pi r_1l_1}{\pi r_2l_2}\\\\\end{gathered}$

$\begin{gathered}\sf \dashrightarrow \dfrac{CSA_1}{CSA_2} = \dfrac{\pi \times\frac{D}{2}\times 4}{\pi \times\frac{D}{2}\times 3}\\\\\end{gathered}$

$\begin{gathered}\displaystyle\sf \dashrightarrow \dfrac{CSA_1}{CSA_2} = \dfrac{4}{3}\\\\\end{gathered}$

$\displaystyle\sf \dashrightarrow CSA_1 : CSA_2 = 4:3$

$\displaystyle\therefore\:\bf{\textsf{The Ratio of their sides will be \textbf{ 4:3 }}}$