Question

6. Fifteen solid spheres are made by melting a solid metallic cone of base diameter 2cm and height 15cm. The radlus of
each sphere is:
(a)½
(b)¼
(c)1/³√2
(d)1/³√4​

Answer 1

Given,

The base diameter of the cone = 2 cm

Height of the cone = 15 cm

Number of spheres = 15

To find,

The radius of each of the sphere.

Solution,

First of all, we have to calculate the volume of the cone by using the following mathematical formula.

Volume of cone = ⅓ × π × (radius)² × height

= ⅓ × π × (2/2)² × 15

= ⅓ × π × 1 × 15

= 5π cm³

Now, let the radius of one sphere = r cm

Volume of one sphere = 4/3 πr³ cm³

According to the question,

15 × 4/3 × πr³ = 5π

r³ = 5π/π × 3/4 × 1/15

r³ = 5 × 1/20

r³ = 1/4

r = 1/³✓4

Hence, the radius of a sphere is 1/³✓4 cm.

Answer 2

Answer:

1/∛4

Step-by-step explanation:

this is the correct ans