Question

A sculptor has just finished creating a large wooden sphere for a sculpture he is working on. The sphere has a radius of 4.3 feet and weighs approximately 10,578.59 pounds. What is the approximate density of the wood used to create the sphere? I need help

Answer 1

The approximate density of the wood used to create the sphere is 0.997 slugs/cubic foot.

Step-by-step explanation:

To find the approximate density of the wood used to create the sphere, we can use the formula for density: density = mass / volume. The volume of a sphere is given by V = (4/3)πr³, where r is the radius of the sphere. In this case, the radius is 4.3 feet, so we can calculate the volume as V = (4/3)π(4.3)^3 = 328.89 cubic feet.

Given that the weight of the sphere is approximately 10,578.59 pounds, we can convert it to mass by dividing by the acceleration due to gravity (g) which is 32.2 feet/second². Mass = weight / g = 10,578.59 / 32.2 = 328.11 slugs.

Using the formula density = mass / volume, we can calculate the density as density = 328.11 / 328.89 ≈ 0.997 slugs/cubic foot.

Answer 2

density = mass/volume

the mass is 10578.9 pounds

the volume of a sphere is v = 4/3 πr^3

v = (4/3) (π) (4.3)^3
v = 333.04

10578.9 / 333.04 = 31.76

the final density is 31.76!!