Question

À solid metallic hemisphere of diameter 21 cm is melted and recasted into a number of smaller Cone,each of diameter 7cm and height 9cm.Find the number of cones so formed.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given:

À solid metallic hemisphere of a diameter of 21 cm

Smaller Cones, each of diameter 7cm and height 9cm

To Find:

The number of cones so formed.

Solution:

Here we will find the volume of the hemisphere and the smaller cone.

To find the number of cones formed, we will divide the volume of the hemisphere by the cone.

volume of hemisphere = (2/3)πr³

where r is the radius

           h is the height

The volume of cone = (1/3)πr²h

where r is the radius and h is the height

Now,

According to the question:

Number of cones formed = $\frac{(2/3)\pi r^{2}h }{(1/3)\pi r^{2} h}$

                                           =$\frac{2\pi (21/2)^{3} }{\pi (7/2)^{2}9 }$

                                           =2(21/2)³/(7/2)²9

                                           = 21

Hence, the number of smaller cones formed is 21