Answer:
226 cm^3
The mass of plastic used to make cylinder is greater
Step-by-step explanation:
Given:-
- The density of cone material, ρc = 1.4 g / cm^3
- The density of cylinder material, ρl = 0.8 g / cm^3
Solution:-
- To determine the volume of plastic that remains in the cylinder after gouging out a hemispherical amount of material.
- We will first consider a solid cylinder with length ( L = 10 cm ) and diameter ( d = 6 cm ). The volume of a cylinder is expressed as follows:
- Determine the volume of complete cylindrical body as follows:
- Where the volume of hemisphere with diameter ( d = 6 cm ) is given by:
- Determine the volume of hemisphere gouged out as follows:
- Apply the principle of super-position and subtract the volume of hemisphere from the cylinder as follows to the nearest ( cm^3 ):
Answer: The amount of volume that remains in the cylinder is 226 cm^3
- The volume of cone with base diameter ( d = 6 cm ) and height ( h = 5 cm ) is expressed as follows:
- Determine the volume of cone:
- The mass of plastic for the cylinder and the cone can be evaluated using their respective densities and volumes as follows:
- The mass of plastic used to make the cylinder ( after removing hemispherical amount ) is:
- Similarly the mass of plastic used to make the cone would be:
Answer: The total weight of the cylinder ( m_l = 180.8 g ) is greater than the total weight of the cone ( m_c = 66 g ).
