Question

Q. A right cone of height 8 cm and base radius 3 cm is converted into some spheres of radius 1 cm.

Then number of sphere is

(a) 72 (b) 36 (c) 18 (d) 24
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Answer 1

Answer:

(c) 18

Step-by-step explanation:

Let the height of cone be h= 8cm and radius be r= 3 cm. Let the radius of sphere be R= 1 cm.

Let the no. of spheres be n.

So,

Volume of cone= Volume of sphere × n

$\binom{1}{3} \pi {r}^{2} h = \binom{4}{3} \pi {r}^{3} \times n$

(r^2) × h = 4R^3 × n

3×3 × 8 = 4 (1^3) × n

n= 3×3×8/4

n = 18

Hence the no. of spheres is 18.

So option (c) is correct.