The diameter of the iron ball used for the shot-put game is 14 cm. It is melted and then a solid cylinder of height `2(1)/(3) cm` is made. What will be the diameter of the base of the cylinder ?

Options

A. 14 सेमी.
B. 28 सेमी.
C. `14/3` सेमी.
D. `28/3` सेमी.

Answer

B

Explanation

बेलन का आयतन = `pi r^2h`
`= pi xx r^2 xx (7)/3`
गेंद का आयतन = `4/3 pir^3 =4/3 xx (7)^3 xx pi`
`4/3 xx (7)^3 xx pi = pi xx r^2 xx 7/3` , अब, प्रश्न से,
`implies 4/3 xx 343 =r^2 xx (7)/3`
`implies r^(2) = (4 xx 343)/7`
`implies r = sqrt(4 xx 49)`
`:. r = 2 xx 7 = 14` सेमी
`:.` बेलन के आधार का व्यास `= 14 xx 2 = 28` सेमी.