SOLUTION: An inverted cone is 3m in radius,7.5m in height. A cube measures 30cm by 30 cm by 30 cm. How many cubes can fit into the inverted cone?

Algebra ->  Volume -> SOLUTION: An inverted cone is 3m in radius,7.5m in height. A cube measures 30cm by 30 cm by 30 cm. How many cubes can fit into the inverted cone?      Log On


   

Question 125931: An inverted cone is 3m in radius,7.5m in height. A cube measures 30cm by 30 cm by 30 cm. How many cubes can fit into the inverted cone?
Answer by marcsam823(57) About Me  (Show Source):
You can put this solution on YOUR website!
1%2F3%2Api%2Ar%5E2%2Ah = Formula for the volume of a cone
x%5E3 = Formula for the volume of a cube
Before we plug numbers into these formulas it is important to note that the units used for the cone's dimensions are in meters and the units for the cube are represented in centimeters. Therefore, we must convert centimeters to meters.
1 cm = 1/100 m
30 cm = 30/100 or 3/10 or .3m
1. Find the volume of the cube:
x%5E3 = .3%5E3 = .3%2A.3%2A.3 = .027m%5E3
2. Find the volume of the cone:
1%2F3%2Api%2Ar%5E2%2Ah = 1%2F3%2Api%2A3%5E2%2A7.5 = 70.69m%5E3
3. To determine how many cubes will fit into the cone:
Volume+of+Cone%2FVolume+of+Cube = 70.69%2F.027 = 2618.14
Answer: 2618 cubes will fit into the cone.