Question

the volumes of two spheres are in the ratio 125:64. Find the ratio of their diameter's

Answer 1

Answer:-

5:4

Step by Step Explanation:-

Let, R and r be the radius of two spheres.

Volume of sphere=4/3πr³

4/3πR³ / 4/3πr³ = 125/64

R³/r³ = 125/64

R/r = 5/8

D/d = 2(5/8)

D/d = 5/4

The ratio of their diameters is 5:4.

Answer 2

Given,

The ratio of the volumes of two spheres = 125:64

To find,

The ratio of the diameters of the two spheres.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the radius of the first sphere is R units and the radius of the second sphere is r units, respectively.

As per mensuration;

i) Diameter of any circle/sphere = 2 × radius

ii) The volume of a sphere = 4/3π(radius)^3

Now, according to the question;

The ratio of the volumes of two spheres = 125:64

=> (volume of the first sphere)/(volume of the second sphere) = 125/64

=> {4/3π(R)^3}/{4/3π(r)^3} = 125/64

=> (R)^3/(r)^3 = 125/64 = (5)^3/(4)^3

=> (R/r)^3 = (5/4)^3

=> R/r = 5/4

{Equation-1}

Now,

The ratio of the diameters of the two spheres

= (diameter of the first sphere)/(diameter of the second sphere)

= {2×(radius the of the first sphere)}/{2×(radius the of the second sphere)}

= (radius the of the first sphere)/(radius the of the second sphere)}

= R/r = 5/4

{according to equation-1}

Hence, the ratio of the diameters of the two spheres is 5:4.