question_answer

A solid metallic cone of height 10 cm, radius of base 20 cm is melted to make spherical balls each of 4 cm diameter. How many such balls can be made?

A)  25                               

B)  75

C)  50                               

D)  125

Correct Answer: D

Solution :

L = the radius of the cone H = height of the cone Volume of cone \[=\frac{1}{3}\pi {{L}^{2}}H\] Let n be the number of spherical balls then volume of the Balls = volume of the cone             \[n\times \frac{2}{3}\pi {{R}^{3}}+\frac{1}{3}\pi {{L}^{2}}H\]             \[n\times 4\pi {{R}^{3}}={{L}^{2}}H\] \[n=\frac{{{L}^{2}}H}{4{{r}^{3}}}=\frac{{{20}^{2}}\times 10}{4\times {{2}^{3}}}\] \[=\frac{400\times 10}{4\times 8}=125\]