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UPSC CDS 2 2022 Math Paper

Consider the following for the next three (03) items that follow :

A conical vessel of radius

12 {cm}

and height

16 {cm}

is filled with water. A sphere is lowered into water and its size is such that it touches the sides of the vessel and .it is just immersed.

Question : 21 of 100

Marks: +1, -0

Solution: 👈: Video Solution

For similar triangles, the ratio of corresponding sides will be equal

Slant height of cone,

1^2=\sqrt{r^2+h^2}

Where,

i=

length,

r=

radius and

h=

height

According to the figure

The slant height of the cone,

(AO)=\sqrt{12^2+16^2}

\Rightarrow \sqrt{144+256}=\sqrt{400}

\Rightarrow AO=20\,\text{cm}

\;\text{In}\;\triangle OBA\sim\triangle OCD

\Rightarrow \;\frac{AB}{CD}=\;\frac{OA}{OD}

\Rightarrow \;\frac{12}{r}=\;\frac{20}{16-r}\;\;[\because OD=OB-BD]

\Rightarrow \;\frac{3}{r}=\;\frac{5}{16-r}

\Rightarrow 48-3r=5r

\Rightarrow 8r=48

\Rightarrow r=6

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