Question

a solid metal cone with radius of base 12cm and height 24 cm is melted to form solid spherical balls of diameter 6m each .the no. of balls formed is _____

Answer 1

Answer

Given : radius of cone = 12 cm and diameter of balls formed = 6 cm(consider error in question)

           height of cone = 24 cm

To find : number of balls

Solution :

Volume of cone = $\bold{\dfrac{1}{3}\pi r^2 h}$

Volume of sphere = $\bold{\dfrac{4}{3}\pi r^3}$

Number of balls = $\bold{\dfrac{Volume \: of \: cone}{ Volume\: of \: sphere}}$

$\implies \bold{\dfrac{\dfrac{1}{3}\pi r^2 h}{\dfrac{4}{3}\pi r^3}}$

$\implies \bold{\dfrac{\dfrac{1}{3}\pi 12^2\times 24}{\dfrac{4}{3}\pi 3^3}}$

$\implies \bold{\dfrac{\pi 144 \times 8}{4\pi 3^2}}$

$\implies \bold{\dfrac{144 \times 8}{4\times 9}}$

$\implies \bold{\dfrac{1152}{36}}$

$\implies \bold{32}$

32 spherical balls will be drawn from the cone .

Thanks

Answer 2

( Radius of cone ( R ) = 12 cm.


Height of cone ( H ) = 24 cm.



Volume of cone = 1/3 πR²H = 1/3 × 22/7 × 12 × 12 × 24 = ( 22 × 12 × 12 × 24 / 3 × 7 ) = (76032/21) cm³.



Diameter of spherical balls = 6 cm




Radius of spherical balls ( R ) = D/2 = 3 cm.





Volume of each spherical balls = 4/3 πR³ = 4/3 × 22/7 × 3 × 3 × 3 = 2376/21.



Number of spherical balls = Volume of cone / Volume of each spherical balls = 76032/21 / 2376/21 = 32.