A wooden pyramid, 9 inches tall, has a square base. A carpenter increases the dimensions of the wooden pyramid by a factor of 4 and makes a larger pyramid with the new dimensions. Describe in complete sentences the ratio of the volumes of the two pyramids

Question

anonymous · Answer

@amistre64

amistre64 · Answer

the area of a cone is 1/3 * basearea * height

amistre64 · Answer

basearea = side^2 in this case

amistre64 · Answer

factor all the linear measures by 4

1/3 * (4s)^2 * 4*9 = 12*16s^2

the original as:

1/3 * s^2 * 9 = 3*s^2

the ratio of the volume is then

3 to 12*16

amistre64 · Answer

reducing by like factors gets us

1 to 4*16

1 to 64