A sphere and a hemisphere have same total surface area- Find the ratio of their radii i-e- r 1- r 2- where r 1 and r 2 are the radii of sphere and hemisphere respectively-A- 1B- -3-4C- -2D- -3-2

The correct option is D √(3)/2 Total surface area of a sphere is nbsp;=4πr_1^2 Total surface area of a hemisphere =3πr_2^2 Since both are equal, nbsp; ...

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Standard VIII

Mathematics

Surface area of a sphere

A sphere and ...

Question

A sphere and a hemisphere have same total surface area. Find the ratio of their radii i.e. $\frac{r_{1}}{r_{2}}$ , where $r_{1}$ and $r_{2}$ are the radii of sphere and hemisphere respectively.

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$\frac{3}{2}$

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$\frac{\sqrt{3}}{4}$

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$\frac{\sqrt{3}}{2}$

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Solution

The correct option is D
$\frac{\sqrt{3}}{2}$

Total surface area of a sphere is
$= 4 π {r_{1}}^{2}$

Total surface area of a hemisphere
$= 3 π {r_{2}}^{2}$

Since both are equal,
$4 π$ ${r_{1}}^{2}$ = 3 $π$ ${r_{2}}^{2}$

$\Rightarrow$ $\frac{{r_{1}}^{2}}{{r_{2}}^{2}}$ = $\frac{3}{4}$

$\Rightarrow$ $\frac{r_{1}}{r_{2}}$ = $\frac{\sqrt{3}}{2}$

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A sphere and a hemisphere have same total surface area. Find the ratio of their radii i.e.r1r2, where r1 and r2 are the radii of sphere and hemisphere respectively.

The correct option is D √32 Total surface area of a sphere is =4πr12 Total surface area of a hemisphere =3πr22 Since both are equal, 4πr12 = 3πr22 ⇒ r12r22 = 34 ⇒ r1r2 = √32​

A sphere and a hemisphere have same total surface area. Find the ratio of their radii i.e. $\frac{r_{1}}{r_{2}}$ , where $r_{1}$ and $r_{2}$ are the radii of sphere and hemisphere respectively.