Knowee
Questions
Features
Study Tools

If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere is

Question

If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere is

🧐 Not the exact question you are looking for?Go ask a question

Solution

The volume of a cube is given by the formula V = s^3, where s is the length of a side of the cube.

The volume of a sphere is given by the formula V = 4/3 * π * r^3, where r is the radius of the sphere.

If a sphere is inscribed in a cube, then the diameter of the sphere is equal to the side length of the cube. Therefore, the radius of the sphere is half the side length of the cube, or r = s/2.

Substituting r = s/2 into the volume formula for a sphere gives V = 4/3 * π * (s/2)^3 = π/6 * s^3.

The ratio of the volume of the cube to the volume of the sphere is therefore (s^3) / (π/6 * s^3) = 6/π.

So, the ratio of the volume of the cube to the volume of the sphere is 6/π.

This problem has been solved

Similar Questions

If the ratio of the volumes of two spheres is 1 : 8. then the ratio of their surface area is

If the surface areas of two spheres are in the ratio of 4 : 25, then the ratio of their volumes is

What is the volume of a sphere with a radius of 5 in, rounded to the nearest tenth of a cubic inch?

Given a sphere with radius r, the formula 4r2 gives _____.A.the volumeB.the surface areaC.the radiusD.the cross-sectional area

If each side of a cube is reduced by 20%, the volume of the cube will be reduced by?40%48.8%60%20%

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.