Download L3 Surface Area and Volume of Right Prisms Part 1

Surface Area and Volume of
Prisms part 1
Cylinder
— SA = sum of areas of bases and lateral surface area
Prism — SA = sum of areas of all faces (bases included)
Pyramid — SA = sum of areas of all faces (bases included)
Lateral Area of a Prism
The lateral area of a prism is the sum of the areas of the lateral faces.
Lateral Face—a lateral face of a prism is a face that joins the bases of the prism
The lateral area of the prism is the total area of its lateral faces.
Lateral Area of a Prism
Suppose the perimeter of the base is p and the height is h.
Lateral Area of a Prism
You can unfold a prism to form a net rectangle.
Lateral Area of a Prism
Notice that the perimeter of the base of the prism is equal to the base of the rectangle and that the
heights are the same.
Lateral Area of a Prism
The lateral area of the prism and the area of the rectangle are equal.
So the lateral area of the prism equals the base of the rectangle
times the height of the rectangle.
Lateral Area = perimeter of base · height of prism
Lateral Area of a Prism
Remember the base of the rectangle equals the perimeter of the
base of the prism and the height of the rectangle is the same as the
height of the prism.
So the lateral area of the prism equals the perimeter of its base p
times its height h.
L.A. = P*h
Surface Area of Prism
The surface area of a prism is the sum of the lateral area and the areas of its
bases.
The surface area of a prism equals the lateral area plus two times the area of a
base.
Surface Area = Lateral Area + 2 · area of a base
Or, SA = LA + 2B
Surface Area of a Cube
The surface area of a cube is the sum of the areas of the
faces of the cube.
Suppose you have a cube with side length s.
Each face of the cube is a square.
The area of a square is the side length squared.
Part 1 Example 1
Find the surface area of each rectangular prism.
Part 1 Example 1
Find the surface area of each rectangular prism.
Part 2 Example 1
Ms. Adventure went on a trip around the world. In the Netherlands, she tasted
Dutch cheese. The piece of cheese has the shape of a triangular prism. How
much surface area is there for mold to grow on?
Part 2 Example 2
What is the surface area of the triangular prism?
Part 3 Example 1
When a base of a prism is a regular polygon, you can decompose the polygon to find its area.
You can decompose a regular hexagon into 6 equilateral triangles.
The 6 triangles are the same size.
After you find the area of 1 triangle, you can multiply the area by 6 to find the area of the entire
hexagon.
Part 3 Example 2
Ms. Adventure wants to make a box like one she saw in Japan. She plans to
cover the box with paper. The box has the shape of a regular hexagonal
prism. To the nearest square inch, how much paper does Ms. Adventure need
to cover the box?
Part 3 Example 3
To the nearest square inch, what is the surface area of the regular hexagonal prism?
Homework:
Surface Area of Prisms Worksheet
Volume of a Prism
Notice that the area of the base of the prism is 20 square units and that the height of
the prism is 3 units.
So the formula for the volume of a prism equals the area of the base times the
height.
Or, V = Bh
Area of the base x height = (length x width) x height
Find the Volume of the Prism.
V = area of base · height
V = Bh
V = (9) (2) (3)
V = 54 ft³
Find the Volume of the Prism.
V = side length cubed
V = s³
V = (3)³
V = (3) (3) (3)
V = 27 ft³
Find the Volume of the Prism.
V = area of base · height
V = Bh
V = (6) (1) (9)
V = 54 ft³
Find the Volume of each Prism.
What is the volume of a cube with edge
length ¾ ft.?
V = side length cubed
V = s³
V = ( 3/4 )³
V = ( 3/4 ) ( 3/4 ) ( 3/4 )
V = 27/64 ft³
Find the Volume the Prism.
V = area of base · height
V = Bh
V = ( 1/2 bh)*h
V = ( 1/2 ) (12) (5) (17)
V = 510 units³
Find the Volume of each Prism.
V = area of base · height
V = Bh
V = ( 1/2 bh) h
V = ( 1/2 ) (4) (3.5) (11.6)
V = 81.2 m³
Find the Volume of the Prism
Ms. Adventure’s Japanese box has the shape of a regular hexagonal
prism. To the nearest cubic inch, what is the amount of space inside
the box?
V = area of base · height
V = Bh
V = 6 ( 1/2 bh)h or (3bh)(h)
V = (6)( 1/2 )(2.6)(3)(4) or (3)(2.6)(3)(4)
V = 93.6 in³
V= 94 in³
Find the Volume of the Prism
V = area of base · height
V = Bh
V = 6( 1/2 bh)h or (3bh)(h)
V = (6)( 1/2 )(6)(5.2)(10.9) or (3)(6)(5.2)(10.9)
V = 1020.24 cm³
HW:
Volume of Prisms Worksheet