Question

a cone is 8.4cm high and the radius of its base is 2.1 cm . it is melted to form a sphere . find the radius of the sphere.

Answer 1

RADIUS OF CONE= 2.1CM
HEIGHT OF THE CONE= 8.4CM

RADIUS OF SPHERE = R
WE KNOW THAT VOLUMES DOES'NT CHANGE WHEN SOME SHAPE IS MELTED AND CONVERTED TO OTHER.

SO, VOLUME OF CONE= VOLUME OF SPHERE
$\frac{1}{3} \pi r^{2} = \frac{4}{3} \pi R^{3}$
$r^{2} h = 4 R^{3}$
$R^{3} = \frac{r^2 h}{4}$
[tex]R^{3} = \frac{(2.1)^2(8.4)}{4} = \frac{4.41*8.4}{4} = 9.261 =\sqrt[3]{9.261} = 2.1CM[/tex]


THE RADIUS OF SPHERE = 2.1 CM




HOPE THIS HELPS........
 

Answer 2

HI there !!

Height = h = 8.4 cm

Radius = r = 2.1 cm

Volume of cone = 1/3πr²h

Volume of the cone = Volume of new sphere

Volume of new sphere = 4/3πr³ 

4/3πr³ = 1/3πr²h

4/3 × 22/7 × r³ = 1/3 × 22/7 × 2.1 × 2.1 × 8.4

4 r ³ = 2.1 × 2.1 × 8.4

r ³ = [ 2.1 × 2.1 × 8.4 ] ÷ 4

r³ = 9.261

r = ∛ 9.261

r = 2.1 cm