Question

# The surface area of a solid metallic sphere is $$\displaystyle 1256cm^{2}$$ it is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm ; then the no. of cones cast $$\displaystyle (\pi =3.14)$$

A
40
B
25
C
48
D
80

Solution

## The correct option is D 80Let the radius of the solid metallic sphere be $$r$$cm$$\therefore 4\pi r^2=1256$$$$=>r^2=\frac{1256}{4\pi}$$$$=>r\simeq10$$cmNow,Volume of the solid metallic sphere=$$\frac{4}{3}\pi r^3$$                                                             =$$\frac{4}{3}\times \frac{22}{7}\times 10^3$$                                                             =$$4190.5 cm^3$$Volume of the solid right circular cone=$$\pi r^2\frac{h}{3}$$                                                                 =$$\pi(2.5)^2\times \frac{8}{3}$$                                                                 =$$52.36 cm^3$$$$\therefore$$ Number of cones casted=$$\frac{4190.5}{52.36}$$                                           $$\simeq 80$$ Mathematics

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