A hollow crystal ball is made of glass that is 3 centimeters thick. The ball has a radius to the outside surface of 8 centimeters.
What is the approximate volume of glass used to make the ball?
Use 3.14 for pi.
Responses
113.0 cm³
113.0 cm³
523.3 cm³
523.3 cm³
1620.2 cm³
1620.2 cm³
2143.6 cm³
2143.6 cm³
To find the approximate volume of glass used to make the ball, we need to find the volume of the entire ball and then subtract the volume of the hollow space inside.
The volume of the entire ball can be calculated using the formula for the volume of a sphere: V = (4/3)πr^3, where r is the radius of the outside surface of the ball.
V = (4/3)π(8 cm)^3
V = (4/3)π(512 cm^3)
V ≈ 2143.6 cm³
Next, we need to find the volume of the hollow space inside the ball. This volume can be calculated similarly but using the radius of the inside surface of the ball, which would be r - thickness of glass = 8 cm - 3 cm = 5 cm.
V = (4/3)π(5 cm)^3
V =(4/3)π(125 cm^3)
V ≈ 523.3 cm³
Finally, to find the volume of glass used to make the ball, we subtract the volume of the hollow space from the volume of the entire ball:
2143.6 cm³ - 523.3 cm³ = 1620.2 cm³
Therefore, the approximate volume of glass used to make the ball is 1620.2 cm³.
Therefore, the correct answer is:
1620.2 cm³