The surface area of a solid metallic sphere is 616 cm2 . It is melted and recast into a solid cone of height 28 cm. Find the diameter of the base of the cone so formed. (Take π=22/7)
Answer & explanation
Correct answer: option 3
We know that,
Surface area of sphere = 4πr2
The volume of the sphere = \(\frac{4}{3}\)πR3
The volume of the cone = \(\frac{1}{3}\)πR2H
We have,
Area of solid sphere = 616 cm2 ,
Height of cone = 28 cm
4πr2 = 616 cm2
then, r2 = 49
r = 7
Volume of sphere = volume of cone
= \(\frac{4}{3}\)πR3 = \(\frac{1}{3}\)πR2H
=4r3 = R2 H
by putting, r = 7 cm , H = 28 cm
= 4×(7)3 = R2 × 28
R = 7
D = 14 cm