Question

The radius of a sphere is multiplied by . What effect does this have on the volume of the sphere? A. The volume of the sphere is multiplied by 1/343. B. The volume of the sphere is multiplied by 1/49. C. The volume of the sphere is multiplied by 1/7 . D. The volume of the sphere is multiplied by 1/21 . E. The effect on the volume of the sphere cannot be determined.

Answer 1

Answer:

Option A. The volume of the sphere is multiplied by 1/343.

Step-by-step explanation:

The volume of a sphere can be obtained by the following formula:

V = 4/3πr^3

Let the initial volume (V1) of the sphere be:

V1 = 4/3πr^3 = (4πr^3)/3

Now, if we multiply the radius by 1/7, then the new volume (V2) of the sphere will be:

V2 = 4/3 x π x (1/7r)^3

V2 = 4/3 x π x 1/343r^3

V2 = (4πr^3)/1029

Now we determine the ratio of V2 : V1 as shown below:

V2/V1 = (4πr^3)/1029 ÷ (4πr^3)/3

V2/V1 = (4πr^3)/1029 × 3/(4πr^3)

V2/V1 = 3/1029

V2/V1 = 1/343

V2 = 1/343 x V1

Therefore, the volume of the sphere is multiplied by 1/343.