Question

Two cones have their base radii in ratio of 3:1 and the ratio of their heights as 1:3. Find the ratio of their surface areas.

Answer 1

Answer:

3:1

Step-by-step explanation:

1 cone radius=3x

2 cone radius=x

1 cone slant height=10x^2^1/2

2 cone " " " """""""=""""""""""""

then CSA =3:1

sorry it's CSA but total surface area also like that ok

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{T.S.A_{1} : {T.S.A_{2} } =6:1}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Ratio \: of \: radius\: of \: cone= 3 :1 \\ \\ \tt: \implies Ratio \: of \: height\: of \: cone= 1 :3\\\\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Ratio \: of \: their \: T.S.A = ?$

• According to given question :

$\circ\:\text{Ratio\:of\:slant\:height\:is\:1}\\\text{because\:their\:radii\:and\:height}\\\text{ratio\:are\:in\:inverse.}\\\\\circ \: \tt{Slant \: height _{1} = Slant \: height_{2}}\\ \\ \bold{as \: we \: know \: that} \\ \tt: \implies \frac{T.S.A_{1}}{T.S.A_{2} } = \frac{\pi r_{1}l_{1} + \pi { r_{1}}^{2} }{\pi r_{2}l_{2} + \pi { r_{2}}^{2}} \\ \\ \tt: \implies \frac{T.S.A_{1}}{T.S.A_{2} } = \frac{\pi r_{1} ( l_{1} + r_{1}) }{\pi r_{2}( l_{2} + r_{2}) } \\ \\ \tt: \implies \frac{T.S.A_{1}}{T.S.A_{2} } = \frac{3(1 + 3)}{1(1 + 1)} \\ \\ \tt: \implies \frac{T.S.A_{1}}{T.S.A_{2} } = \frac{12}{2} \\ \\ \tt: \implies \frac{T.S.A_{1}}{T.S.A_{2} } = \frac{6}{1} \\ \\ \green{\tt: \implies {T.S.A_{1}} : {T.S.A_{2} } =6 : 1}$