Question

If a cone and a sphere have the same radius and the same height what is the relationship among the volumes of the two shapes

Answer 1

V (cone) = πR².H/3

V (sphere) =(4/3).π.R³

Given: Same Radius and cone a nd sphere same H =2R. Replace H with 2R

V (cone) = πR².(2R)/3 = 2πR³/3

Then V (sphere)[ = (4/3).π.R³]= 2 V (cone) [ = 2πR³/3]

Answer 2

the volume of the sphere will be 4 times the volume of the cone;

Explanation:

The question is on volume comparison

Volume of a sphere=4/3 ×r³

Volume of a cone= /3×r²h

where r is the radius and h is the height

Apply the condition

If r=h=1 unit

Then volume of sphere will be= 4/3 × ×1³ = 4/3

And volume of the cone will be= /3 ×1²×1 =/3

We can see the volume of the sphere will be 4 times the volume of the cone;

4/3 = 4×/3