Question

504 cones, each of diameter 3.5 cm and height 3 cm, are melted and recast into a metallic sphere. Find the diameter of the sphere and hence find its surface area. [u

Answer 1

Answer:

Given

diameter of cone = 3.5 cm

height = 3 cm

Volume of cone=  1/3×$\pi$×r$^{2}$h

=> 1/3× 22/7× 3.5/2×3.5/2 ×3

=> Volume of cone=  77/8

cones are melted and made into a sphere..

Volume of sphere = 4851 cm $^{3}$  

4/3 ×$\pi$  ×r$^{3}$  

=> 4851

=> 4/3 × 22/7 ×  r $^{3}$        

=> r$^{3}$  = 1157.625cm

r= 10.5 cm

Diameter = 2r

Diameter = 2×10.5= 21 cm

Total surface area of sphere = 4 × π × r²  

total surface area cone  = 4 × 22/7× 10.5× 10.5

=>  1386 cm$^{2}$

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@GauravSaxena01