1.

2 metallic right circular cones having their height 4.1cm and 4.3cm respectively and the radii of their bases 2.1cm each have been melting together and recasted into a shpere determine the diameter of the sphere so formed

Answer»

The diameter of the SPHERE so formed is 6.66 CM

Step-by-step explanation:

Cone 1 :

HEIGHT of cone = 4.1 cm

Radius of cone = 2.1 cm

Volume of cone = \frac{1}{3} \pi r^2 h =\frac{1}{3} \times \frac{22}{7} \times 2.1^2 \times 4.1 =18.942 cm^3

Cone 2 :

Height of cone = 4.3 cm

Radius of cone = 2.1 cm

Volume of cone = \frac{1}{3} \times \frac{22}{7} \times 2.1^2 \times 4.3 =19.866 cm^3

Volume of sphere = \frac{4}{3} \pi r^3 =\frac{4}{3} \times \frac{22}{7} \times r^3

Two CONES are melted to form sphere

So, volume of two cones will be equal to the volume of sphere

So, \frac{1}{3} \times \frac{22}{7} \times 2.1^2 \times 4.1 +\frac{1}{3} \times \frac{22}{7} \times 2.1^2 \times 4.3 =\frac{4}{3} \times \frac{22}{7} \times r^3\\\\ 2.1^2 \times 4.1 + 2.1^2 \times 4.3 =r^3\\\\ \sqrt[3]{2.1^2 \times 4.1 + 2.1^2 \times 4.3 }=r\\\\3.33=r

So, radius of sphere = 3.33 cm

Diameter of sphere =3.33 \times 2 = 6.66

HENCE the diameter of the sphere so formed is 6.66 cm

#Learn more :

2 metallic circular cones having their heights 4.1 cm and 4.3 cm and the radii of their bases 21 cm each have been melted together and recast into a sphere. Find the diameter of the sphere.

brainly.in/question/2487748


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