Question

504 cones of diameter 3.5 cm and height 3cm each melted to form sphere. find the diameter of sphere and surface area

Answer 1

504 x volume of cone = volume of sphere

504 x pi.(7/4)^2 x( 3/3) = 4/3 pi.R^3
504 x 49/16 x 1 = 4/3 R^3
7 x72x 3 x 7 x 7 /64 = R^3

R=7 x 6 /4 =21/2 cm
so, diameter = 21 cm

now,
surface area of sphere =4 x 22/7 x (21/2)^2
= 4 x 22/7 x 441/4
= 22 x 63
=1386 cm^2

Answer 2

no. of cones × volume of 1 cone=volume of sphere
=>504×1/3 πr^2h= 4/3 πr^3
=> 504×1/3 × 22/7×3.5/2×3.5/2 × 3= 4/3 × 22/7 × r^3
(now the 1/3 and 22/7 from both sides gets cancelled)
r^3=3.5×3.5×3×504/2×2×2
r=21/2
d= 21cm