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3 – Dimensional Shapes
2 bases:
prism, named by the shape of its bases
all other shapes are rectangles
1 base:
pyramid, named by the shape of its base
all other shapes are triangles
In the figure below, describe the base, name the figure,
and name the part labeled CD.
SolidsSolids
The base is a rectangle.
The figure is a rectangular pyramid.
CD is a base edge.
Rectangular Prisms
20
7
4
Front _______
Back________
Side ________
Side ________
Top ________
Bottom_______
Total Surface Area: _________
You try
15
53
Front _______
Back________
Side ________
Side ________
Top ________
Bottom_______
Total Surface Area: _________
You try
11
7
21
Front _______
Back________
Side ________
Side ________
Top ________
Bottom_______
Total Surface Area: _________
Kevin wants to paint the walls and ceiling of room. His room is 11 feet long, 12 feet wide and 8 feet high. How many square feet will he cover?
One gallon of paint will cover 200 ft² of surface area. How many gallons of paint does Kevin need to buy to paint his room?
Alisha wants to paint the walls of her bedroom. Her room is 18 feet long, 14 feet wide, and 10 feet high. The paint she decides to buy will cover 100 square feet. How many gallons will she need?
EXIT QUESTION
John wants to paint the walls of his kitchen. The kitchen is 10 feet long, 12 feet wide, and 11 feet tall.
How many square feet will his paint need to cover?
EXIT
A snack bar is offering two types of drinks. The first drink, “The Barrel” is cylindrical in shape with a diameter of 3 inches and a height of 10 inches. The second drink, “The Boxer,” is rectangular in shape with a square bottom of 3 inches per side and a height of 8 inches. If both drinks cost $1.99, which one is a better value? Why?
The cube shown below has a surface area of 150 square inches.
What is the length of each side of the cube?
The cube shown below has a surface area of 600 square inches.
What is the length of each side of the cube?
Find the volume of a cylindrical cake that is 5 in. tall with a diameter of 15 in. Give your answer to the nearest whole unit.
884 in.³
CHANGING DIMENSIONS:
Changing the length, width, height, or radius
SCALE FACTOR:
The number multiplied by the original figure/amount to get the new figure/amount
EXAMPLE:
4
6
By what scale factor will the area of the triangle increase if the base is doubled and the height is tripled?
If the length of the side of a square is doubled, what would happen to its perimeter?
a. It doubles
b. It triples
c. It quadruples
d. It gets smaller
If the length of the side of a square is doubled, what would happen to its area?
a. It doubles
b. It triples
c. It quadruples
d. Nothing happens
If the length of the radius of a square is doubled, what would happen to its area?
a. It doubles
b. It triples
c. It quadruples
d. Nothing happens
When one dimension is changed…
If you double the height of the prism
What happens to the following:
1. Surface area?
2. Volume?
32
5
The surface area of a cube is 150 square inches.
If you double the length of each side what is the new surface area?
By what scale factor will the surface area by reduced if the length of each side is reduced by half?
The Graf company produces cylindrical barrels.
If the height of a barrel is reduced from 21 feet to 7 feet, what will happens to the volume of the barrel?
A.The volume triples.
B.The volume doubles.
C.The volume is reduced to one half of the original.
D.The volume is reduced to one third of the original.