The diameter of earth is 7917.5 mi and the diameter of mercury is 3032 mi. how many times can mercury go inside earth. use 3.14 for pi, round to nearest tenth

Mercury can enter 6.8 times inside the earth

Step-by-step explanation:

To solve this problem we have to calculate the volumes

First we calculate the radius

radius earth = 7917.5mi /2 = 3958.75mi

radius mercury = 3032mi / 2 = 1516mi

To calculate the volume of earth we have to use the following formula:

V = volume

r = radius  = 3958.75mi

π = 3.14

V = ⁴⁄₃πr³

we replace with the known values

V = ⁴⁄₃ * 3.14 * (3958.75mi)³

V = 4.187 * 15671701.56 mi³

V =  65617414 mi³

The volume of earth is 65617414 mi³

To calculate the volume of mercury we have to use the following formula:

V = volume

r = radius  =  1516mi

π = 3.14

V = ⁴⁄₃πr³

we replace with the known values

V = ⁴⁄₃ * 3.14 * ( 1516mi )³

V = 4.187 * 2298256 mi³

V =  9622797 mi³

The volume of mercury is 9622797 mi³

Now we divide the earth volume by the mercury volume

65617414 mi³  / 9622797 mi³  = 6.819

round to the nearest tenth

6.819 = 6.8

Mercury can enter 6.8 times inside the earth

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

answer: sensy

step-by-step explanation: