Q:Sabrina is making two bird feeders in the shape of right rectangular prisms. The smaller feeder has dimensions that are 1/4 of the dimensions of the larger feeder. Using the formula V=lwh, how do their volumes compare???
A:
A) The volume of the larger feeder is 4 times as great as the volume of the smaller feeder.
B) The volume of the larger feeder is 12 times as great as the volume of the smaller feeder.
C) The volume of the larger feeder is 64 times as great as the volume of the smaller feeder.
D) The volume of the larger feeder is 82 times as great as the volume of the smaller feeder.
Can someone help check this for me???
I believe the answer is B but I am really unsure....
if the sides scale by 4, the volume scales by 4^3=64, so (C)
You can see why this is, since the original volume is
v = lwh
Now, with each dimension scaled by 4,
V = (4l)(4w)(4h) = 4*4*4(lwh) = 4^3 v
To compare the volumes of the two bird feeders, we need to know the dimensions of both feeders. The problem states that the dimensions of the smaller feeder are 1/4 of the dimensions of the larger feeder.
Let's assume the dimensions of the larger feeder are l, w, and h. Then, the dimensions of the smaller feeder would be (1/4)l, (1/4)w, and (1/4)h.
Now, let's calculate the volumes of the two feeders using the formula V = lwh.
Volume of the larger feeder = lwh
Volume of the smaller feeder = (1/4)l * (1/4)w * (1/4)h = (1/64)lwh
To compare the volumes, we can divide the volume of the larger feeder by the volume of the smaller feeder:
Volume of the larger feeder / Volume of the smaller feeder = (lwh) / ((1/64)lwh) = 64
Therefore, the volume of the larger feeder is 64 times as great as the volume of the smaller feeder.
So, the correct answer is C) The volume of the larger feeder is 64 times as great as the volume of the smaller feeder.