Solids

Words of “Wiz-dom”-You’ll only see two possible shapes of solids. The most common is a rectangular (or cubic) solid. Keep in mind that its surface area and perimeters of individual faces are the same as rectangles and squares. The less common type of solid is a right cylinder. That’s a can! It is simply a pair of identical circles connected by a rectangle that has been rolled into a tube. Prove it to yourself by forming a tube with a piece of paper. Notice you formed a circle with an edge of the paper. What used to be a straight line is now a circumference!

Rectangular Solids

The following questions relate to the solid above for which the height is 3, the length is 6, and the width is 4.

What is the volume of the solid? Answer #1

What is the surface area of the solid? Answer #2

What is the length of the diagonal AB of the end? Answer #3

What is the perimeter of the top (or bottom)? Answer #4

What is the ratio of the height to the length? Answer #5

If an ant walks only on the edges, what is the length of the shortest route from A to C? Answer #6

Right Cylinders

The following questions relate to the solid above for which the height is 8 and the radius is 3.

What is the volume?
Answer #7

What is the surface area?
Answer #8

What is the circumference?
Answer #9

What is the shortest distance from A to B (points exactly opposite one another?)
Answer #10

If an ant runs around the top rim, then straight down the side, then runs around the bottom rim, how far did she go?
Answer #11

Sample Questions

1. If the length of the side of a cube is doubled, what effect does it have on the surface area of the cube?

A. 2 times as large
B. 4 times as large
C. 12 times as large
D. 24 times as large
E. 48 times as large

Answer to question #1

2. If the height of a right cylinder is tripled and its radius is doubled, how much larger is the volume?

A. 5 times larger
B. 6 times larger
C. 12 times larger
D. 16 times larger
E. 24 times larger

Answer to question #2

3. A painter is going to paint the walls of The Wiz’s cogitating room that is 12 feet wide and 18 feet long. The walls are 8 feet high. He can cover 400 square feet of surface area with each gallon of paint. If he can only buy whole gallons of paint, how many gallons does he need to purchase?

A. 1
B. 2
C. 3
D. 4
E. 5

Answer to question #3

4. What is the most number of small cubes with an edge of 15 that will fit in a large cube with an edge of 75?

A. 5
B. 25
C. 100
D. 125
E. 250

Answer to question #4

5. A cube has a volume of 27. What is its surface area?

A. 9
B. 24
C. 36
D. 54
E. 81

Answer to question #5

6. A rectangular solid has a length of 12, a height of 8, and a width of 6. What is the minimum length of tape needed to cover all of the edges without overlap?

A. 26
B. 52
C. 96
D. 104
E. 132

Answer to question #6

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