Question

A cone is 8.4 cm high and the radius of its base is 2.1 cm. This is melted to be cast in the shape of a sphere. Find the radius of the sphere.​

Answer 1

$\huge\mathfrak{Solution:}$

Here, height of the cone, h = 8.4 cm,

radius of the base of the cone, r = 2.1 cm

Suppose, the radius of the sphere = r1 cm

Since sphere is casted by melting the cone

Therefore, volume of the cone = volume of the sphere

Therefore, 1/3 × pi × r^2 × h = 4/3 × pi × r1^3
[volume of the cone = 1/2 × pi × r^2 × h and that of sphere = 4/3 × pi × r1^3]

or r^2 × h = 4 × r1^3

or (2.1)^2 × 8.4 = 4 × r1^3

or 2.1 × 2.1 × 8.4 / 4 = r1^3

or r1 = cube root 2.1 × 2.1 × 2.1

Therefore, r1 = 2.1

Hence, radius of the sphere = 2.1 cm

__________________________

HOPE IT HELPS ❤❤

Answer 2

Answer:

Here hieght (h)=8.4cm &radius of base(r)=2.1

Step-by-step explanation:Now volume the cone =1/3*22/7*2.1*2.1*8.4

now let radius of the sphere =R

therefore volume the sphere=4/3*22/7*R^3

Again BYE THE PROBLEM:

volume of the sphere =volume of the cone

Therefore solved