A Cone-shaped piece of paper has a height of 15 centimeters and a radius of 1.2 centimeters. The cone is 2/3 filled with sand. What is the approximate volume of the portion of the cone not filled with sand?
Volume of a Cone:
V = πr²h/3
Since 2/3 is filled with sand, 1/3 must not be filled with sand.
V = 1/3 [π(1.2 cm)²(15 cm)/3]
V = 7.54 cm³
To find the volume of the portion of the cone not filled with sand, we first need to find the volume of the entire cone, and then subtract the volume of the sand-filled portion.
The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius and h is the height.
Given:
- Radius (r) = 1.2 centimeters
- Height (h) = 15 centimeters
First, let's calculate the volume of the entire cone:
V_cone = (1/3)π(1.2²)(15)
≈ 7.2π cm³
Now, we need to find the volume of the sand-filled portion. We are told that the cone is 2/3 filled with sand, which means the remaining 1/3 is not filled with sand.
Volume of sand-filled portion = (2/3) * V_cone
= (2/3) * 7.2π cm³
≈ 4.8π cm³
Finally, to find the volume of the portion of the cone not filled with sand:
Volume not filled with sand = V_cone - Volume of sand-filled portion
= 7.2π cm³ - 4.8π cm³
= 2.4π cm³
Therefore, the approximate volume of the portion of the cone not filled with sand is 2.4π cubic centimeters.