Question

‼️GEOMETRY‼️

What is the approximate surface area of the largest sphere that can fit inside a cube with a side length of 18 inches?

1018 square inches
1356 square inches
4069 square inches
6104 square inches

Answer 1

A.) 1018 square inches

Explanation:

The largest sphere will have a diameter equaling the length of the cube (see picture).

If the side length of the cube is 18 inches, the diameter of the sphere is also 18 inches. Use the surface area formula for a circle:

`SA=4\pi r^2`

For this formula, we need the radius of the sphere. Divide the diameter by 2:

`(18)/(2)=9`

The radius is 9 inches. Plug this into the equation:

`SA=4\pi *9^2`

Simplify the equation:

`SA=4\pi *81\\\\SA=324\pi \\\\SA=1017.87`

Round the result to the nearest whole number:

`1017.87` →
`1018`

The surface area is 1,018 inches².

:Done

Picture:

In a 2D version, we can clearly see that if the circle fits snuggly inside of the square, the diameter of a sphere is the same as the length of a side of the cube.