??Jack has two spheres one has radius of 12 and the other has a diameter of 12. What is the difference between two spheres?
Diameter=2*Radius
Radius=Diameter/2
Radius of first sphere R1=12
Radius of second sphere R2=D2/2=12/2=6
R1/R2=12/6=2
R1/R2=2
Area of sphere=4*pi*R^2
Area of first sphere A1=4*pi*12^2=
4*pi*(2*6)^2=4*pi*4*6^2
Area of second sphere A2=4*pi*6^2
A1/A2=(4*pi*4*6^2)/(4*pi*6^2)=4
A1/A2=4
Volume of a sphere:
V=(4/3)*pi*R^3
Volume of first sphere:
(4/3)*pi*12^3=
(4/3)*pi*(2*6)^3=(4/3)*pi*8*6^3
Volume of second sphere:
(4/3)*pi*6^3
V1/V2=[(4/3)*pi*8*6^3]/[(4/3)*pi*6^3]=8
V1/V2=8
V2/V1=8
First sphere have 2x larger Radius, 4x larger Area and 8x larger Volume
V1/V2=8
Delete: V2/V1=8
To find the difference between the two spheres, we first need to calculate their volumes. The volume of a sphere is given by the formula V = (4/3) * π * r^3, where r is the radius.
For the first sphere with a radius of 12, the volume would be V1 = (4/3) * π * 12^3.
For the second sphere, since we know the diameter is 12, which is twice the radius, we can calculate the radius as 12 / 2 = 6. So the radius of the second sphere is 6.
Now, let's calculate the volume of the second sphere, V2 = (4/3) * π * 6^3.
To find the difference between the volumes, we can subtract V2 from V1, which gives us V1 - V2.
Now, let's calculate the volumes and find the difference:
V1 = (4/3) * 3.14 * 12^3
V1 = (4/3) * 3.14 * 1728
V1 ≈ 7238.23
V2 = (4/3) * 3.14 * 6^3
V2 = (4/3) * 3.14 * 216
V2 ≈ 904.32
Now, find the difference between the two volumes:
Difference = V1 - V2
Difference = 7238.23 - 904.32
Difference ≈ 6333.91
So, the difference between the volumes of the two spheres is approximately 6333.91.