The lengths, widths, and heights of both rectangular prisms must have the same proportion to be similar. They've got to be exactly identical if they're congruent.
Answer
The solids are neither similar nor congruent.
Example 2
Are the cylinders similar, congruent, or neither?
Hint
It's not a Herculean task; it's a Pythagorean task.
Answer
The two cylinders are congruent.
Example 3
Are the spheres similar, congruent, or neither?
Hint
Spheres only have one measurement to compare, so they'll always be similar at the very least. If they're congruent, their scale factor will be 1.
Answer
The two spheres are congruent.
Example 4
Pluto might not be considered a planet anymore, but we can still send a little love. The diameter of Pluto is about five times smaller than Earth's 7913-mile diameter. If that's the case, what is Pluto's approximate volume?
Hint
The scale factor is 0.2 or 1:5. Also, volume will be in units of miles cubed, not decibels.
Answer
Pluto's volume is about 2,075,449,194 cubic miles.
Example 5
It's common knowledge that Old MacDonald had a farm, but he actually had a barn for cows as well. Before he built the barn, he wanted a scale model that was 1:100. If the scale model had the dimensions listed, how big is Old MacDonald's barn in cubic feet? There are 12 inches in a foot and 4 feet per cow (except Bessie, who was in a tragic cattle guard accident).
Hint
Find the volume of the scale model (sum up the rectangular and triangular prisms) in inches cubed. Then convert to the life-size barn.
Answer
The volume of Old MacDonald's barn is about 354,167 feet cubed.
Example 6
A miniature replica of an Egyptian pyramid is made, for the mummified mice. If the base of the pyramid is 700 feet long and the height is 450 feet and the replica's base is 3 inches long, how tall is the mini-pyramid?
Hint
Use the base edge to find the scale factor. Use the scale factor to find the height. Also, remember that a foot has 12 inches.
