Question

If a sphere is placed in a cone of height 9 cm, then the volume of sphere if it
touches lateral surface and base of a cone is?​

Answer 1

Volume of sphere =  113.09 cm³

Given:

A sphere is placed in a cone of height 9 cm.

To find:

The volume of sphere if it  touches lateral surface and base of a cone is?​

Explanation:

See the below attached image.

In, △OCD=,∠COD=30°

∴sin30°=  $\frac{CD}{DO}$   = $\frac{1}{2}$ ⇒    $\frac{CD}{9}$  =  $\frac{1}{2}$​  

                          = CD=4.5cm

We know that △OAB∼△OCD

  $\frac{OA}{OC}$ =    $\frac{AB}{CD}$ ⇒    $\frac{9-AB}{9}$ =   $\frac{AB}{4.5}$  [∵OC=OA+AC=OA+AB]

⇒40.5− 4.5 AB = 9 AB ⇒ 13.5 AB = 40.5

                                             AB  =  $\frac{40.5}{13.5}$ = 3 cm

AB is the radius of the sphere.

Volume of sphere= $\frac{4}{3}$ ×$\pi$ × R³

                              = $\frac{4}{3}$ × π×3×3×3=  36π cm³  = 113.09 cm³

To learn more....

1)The volume of sphere is 792/7 cm3 . determine its diameter.

https://brainly.in/question/6890984

2)If radius of a sphere is 23cm find the volume of the sphere.

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