Question

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compare 2 spheres. The first has a diameter of 4 milimeters. The second sphere has a diameter of 596 milimeters. Determine the ratio of the volume of the large sphere to the volume of the small sphere.

Answer 1

The volume of a sphere is given by the formula

Volume = 4/3 * pi * r^3

where r is the radius of the sphere.

The radius of the first sphere is 2 mm, so its volume is

4/3 * pi * 2^3 = 33.51 mm^3

The radius of the second sphere is 298 mm, so its volume is

4/3 * pi * 298^3 = 4,047,000 mm^3

The ratio of the volumes of the two spheres is

4,047,000 mm^3 / 33.51 mm^3 = 121,360

Answer 2

Answer: V₂:V₁=3307949:1

Explanation:

`\displaystyle\\\boxed {V=(4)/(3)\pi r^3 }\\`

`\displaystyle\\d_1=4\ mm\ \ \ \ \Rightarrow\ \ \ \ r=(4)/(2)=2\ mm`

`\displaystyle\\V_1=(4\pi (2)^3)/(3)`

`\displaystyle\\d_2=596\ mm\ \ \ \ \ \Rightarrow\ \ \ \ \ r=(596)/(2)=298\ mm`

`\displaystyle\\V_2=(4\pi (298)^3)/(3)\\\\(V_2)/(V_1)=((4\pi (298)^3)/(3) )/((4\pi (2)^3)/(3) ) \\\\(V_2)/(V_1)=(298^3)/(2^3) \\\\(V_2)/(V_1) =((298)/(2) )^3\\\\(V_2)/(V_1)=((149)/(1) )^3 \\\\(V_2)/(V_1)=(149^3)/(1^3) \\\\V_2:V_1=3307949:1`