Question

the sphere at the right fits snugly inside a cude with 14in edges. what is the approximate volume of the space between the sphere and the cube?​

Answer 1

Answer:Find the vol of the sphere:

radius of the sphere = 3 in

V = %284%2F3%29%2Api%2A3%5E3

V = 97.858

:

Find the vol between the sphere and cube:

216 - 97.858 = 118.142 cu/in

Step-by-step explanation:

Answer 2

The approximate volume of the space between the sphere and the cube is 1308 cubic inches.

Step-by-step explanation:

The volume of a cube with side length 14 inches is calculated by multiplying the length, width, and height:

14 × 14 × 14 = 2744 cubic inches.

The volume of a sphere is calculated using the formula :

`V = (4)/(3)  * \pi * r^3`, where r is the radius.

In this case, the diameter of the sphere is equal to the side length of the cube, so the radius is half of the diameter, which is 7 inches. Plugging in the values, the volume of the sphere is approximately :

[tex]V = \frac{4}{3} \times \pi \times 7^3[/tex} = 1436 cubic inches.

To find the approximate volume of the space between the sphere and the cube, subtract the volume of the sphere from the volume of the cube: 2744 - 1436 = 1308 cubic inches.

Therefore, the approximate volume of the space between the sphere and the cube is 1308 cubic inches.