Question : A frustum of a right circular cone, whose height is 18 cm, large base radius is 25 cm, and small base radius is 20 cm, is melted to form a small sphere of diameter 2 cm. How many spheres will be formed?
Option 1: 6287
Option 2: 6862
Option 3: 4575
Option 4: 5857
Correct Answer: 6862
Solution :
Here, the height of the frustum ($h$) = 18 cm
Large base radius ($R$) = 25 cm
Small base radius ($r$) = 20 cm
So, the volume of the frustum
= $\frac{\pi h}{3}(R^2+Rr+r^2)$
= $\frac{\pi×18}{3}(25^2+25×20+20^2)$
= $9150\pi\ \text{cm}^3$
Now, radius of the sphere = $\frac{2}{2}$ = 1 cm
the volume of one sphere = $\frac{4}{3}\pi (1)^3$ = $\frac{4}{3}\pi\ \text{cm}^3$
$\therefore$ the number of required sphere = $\frac{9150\pi}{\frac{4}{3}\pi}= 6862.5 \approx 6862\ \text{cm}^3$
Hence, the correct answer is 6862.
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