Question

504 cones each of diameter 3.5cm and height 3 cm melted and recast into a metallic sphere. find the diameter of the sphere and hence find the total surface area of the sphere .(take pie=22/7

Answer 1

diameter of cone = 3.5 cm and height = 3 cm

Volume of cone = $\frac{1}{3} * \pi * r^2 h$

                = $\frac{1}{3} * \frac{22}{7} * \frac{3.5}{2} * \frac{3.5}{2} * 3$
             = $\frac{77}{8}$

Volume of 505 cones = 504 * 77/8 = 4851 cu cm
 
 These cones are melted and made into a sphere..

Volume of sphere = 4851 cu cm              

$\frac{4}{3} * \pi * r^3 = 4851$

$\frac{4}{3} * \frac{22}{7} * r^3 = 4851$


r³ = 1157.625

r = 10.5 cm

Diameter = 21 cm

Total surface area of sphere = 4 * π * r² 

TSA = 4 * 22/7 * 10.5 * 10.5 = 1386 sq cm

Answer 2

height of cone = 3 cm 
diameter of cone = 3.5 cm or radius = 3.5/2