The volume of first sphere = 27 x volume of second sphere
Let the radius of the first sphere = r1 and, radius of second sphere = r2
(i) Then, according to the question we have
![\[\begin{array}{*{35}{l}} 4/3\text{ }\pi {{r}_{1}}^{3}~=\text{ }27\text{ }\left( 4/3\text{ }\pi {{r}_{2}}^{3} \right) \\ {{r}_{1}}^{3}/\text{ }{{r}_{2}}^{3}~=\text{ }27 \\ {{r}_{1}}/\text{ }{{r}_{2}}~=\text{ }3/\text{ }1 \\ Thus,\text{ }{{r}_{1}}:\text{ }{{r}_{2~}}=\text{ }3:\text{ }1 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-408bab3fbe875ba39170d741c31d55d8_l3.png "Rendered by QuickLaTeX.com")
(ii) Surface area of the first sphere = 4 πr12
And the surface area of second sphere = 4 πr22
Ratio of their surface areas
![\[=\text{ }4\text{ }\pi {{r}_{1}}^{2}/\text{ }4\text{ }\pi {{r}_{2}}^{2}~=\text{ }{{r}_{1}}^{2}/\text{ }{{r}_{2}}^{2}~=\text{ }{{3}^{2}}/\text{ }{{1}^{2}}~=\text{ }9\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-80b3c124a23e039e689e6a9cf64bdf9c_l3.png "Rendered by QuickLaTeX.com")
Hence, the ratio = 9: 1
and 
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. for which the area of a ABC having vertices 
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is 35 sq units. for which the points 
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