Take an open box, four sets of marbles (marbles in each set have the same size) and water. Place the marbles and water in the box and attempt the question- do larger marbles or smaller marbles occupy more volume in a given space
Answers
Answer:
You would simply find the volume of each size of marble and multiply them by 6 to determine the total volume taken by each set of marbles. On the other hand, if you just want to know how much more volume one takes over the other, you just need to compare the cube of the radii: For example:
Let s = the radius of the smaller marble = 1cm
Let l = the radius of the larger marble = 2cm
V_s=4/3pi(1)^3=4/3pi
V_l=4/3pi(2)^3=32/3pi
Total volume taken by six smaller marbles = 6(4/3pi)=8pi
Total volume taken by six larger marbles = 6(32/3pi)=64pi
How many times the volume of the smaller marbles do the larger marbles multiply:
(6(32/3pi))/(6(4/3pi))=(32/3pi)/(4/3pi)=32/4=8
Therefore, the larger marbles take up 8 times more space than the smaller marbles.
Answer:
You would simply find the volume of each size of marble and multiply them by 6 to determine the total volume taken by each set of marbles. On the other hand, if you just want to know how much more volume one takes over the other, you just need to compare the cube of the radii: For example:
Let s = the radius of the smaller marble = 1cm
Let l = the radius of the larger marble = 2cm
V_s=4/3pi(1)^3=4/3pi
V_l=4/3pi(2)^3=32/3pi
Total volume taken by six smaller marbles = 6(4/3pi)=8pi
Total volume taken by six larger marbles = 6(32/3pi)=64pi
How many times the volume of the smaller marbles do the larger marbles multiply:
(6(32/3pi))/(6(4/3pi))=(32/3pi)/(4/3pi)=32/4=8
Therefore, the larger marbles take up 8 times more space than the smaller marbles.
Step-by-step explanation: