Download The LATERAL SURFACE AREA ("shell") of a general cylinder is the

Aim #6 How do we calculate lateral and surface area of prisms and
cylinders?
CC Geo R
Do Now: Calculate the volume of the figures below. Leave in terms of pi if
necessary.
10
12
8
16
14
The LATERAL SURFACE AREA ("shell") of a general cylinder is the product of
the perimeter of one cross section and the height of the cylinder.
*If the general cylinder has a circular base, perimeter = circumference.*
Lateral Surface area of a cylinder = height perimeter of a base
Examples:
5
15
12
12
10
9
20
7
Total Surface Area of a cylinder = Lateral Area + Area of two bases
Examples:
5
12
15
9
12
7
10
20
1
Exercises: Lateral and Surface Area
1. The base of the following right cylinder has a circumference of 5π and a lateral
edge of 8. What is the radius of the base? What is the lateral area of the right
cylinder? (in terms of π) What is the surface area?
2. The following right general cylinder has a lateral edge length of 8 and the
perimeter of its base is 27. What is the lateral and surface area of the right
general cylinder?
3. The base of the following right cylinder has a diameter of 12 and a lateral edge
of 8.6 cm. Calculate the lateral and surface area of the right cylinder, to the
nearest tenth.
4. The following right prism has trapezoidal base regions; it is a right trapezoidal
prism. The lengths of the edges of the parallel bases are 8 and 5 and the non
parallel edges are 4 and 6 and the height of the trapezoid is 3.7. The lateral edge
length DH is 10. Find the total surface area, to the nearest tenth.
[Area of trapezoid = ½h(b1 + b2) ]
2
5) Find the exact surface area.
8
8
12
8
6) How much glass is needed to construct a fish tank in the shape of a rectangular
prism with a length of 1.25 feet, a width of 1 foot and a height of 8 inches. (keep in
mind the top of the tank is left open)
Let's Sum it Up!!
The lateral area of a general cylinder is the product of the perimeter of the
base times the height of the cylinder
The surface area of a general cylinder is the lateral area plus the area of
the two bases.
3
4
Name_____________________________
Date ____________________
CC Geometry R
HW #6
1) The base of the following right cylinder has a circumference of 8π and a
lateral edge of 12. What is the radius of the base? What is the lateral and
surface area of the right cylinder (in terms of π)?
r = 4
LA 96π
SA = 128π
2) The following right general cylinder has a lateral edge length of 10 and the
perimeter of its base is 40. What is the lateral area and surface area of the right
general cylinder?
LA = 400 un2
3) A right square prism has base edge 6 and height 24. Find the surface area of
the prism.
SA = 648 un2
2
3
4) A cross-section of a prism has area 84 cm . If the volume of the prism is 273 cm ,
what is the exact height of the prism?
h = 3.25 cm
5
5) What is the exact surface area of the triangular prism shown below.
12
SA = 720 + 72√3
12
20
12
6) Find the total surface area and volume of the oblique cylinder. (in terms of π)
SA = 252π un2
V = 540 π un3
Review
1) Solve for the measure of the missing sides. Round to the tenth place.
y
12
x = 11.2
47
x
y = 16.4
2) Solve for the measure of the missing angle. Round to the nearest degree.
31o
12
x
14
6
Name_____________________________
Date ____________________
CC Geometry R
HW #6
1) The base of the following right cylinder has a circumference of 8π and a
lateral edge of 12. What is the radius of the base? What is the lateral and
surface area of the right cylinder (in terms of π)?
2) The following right general cylinder has a lateral edge length of 10 and the
perimeter of its base is 40. What is the lateral area and surface area of the right
general cylinder?
3) A right square prism has base edge 6 and height 24. Find the surface area of
the prism.
2
3
4) A cross-section of a prism has area 84 cm . If the volume of the prism is 273 cm ,
what is the exact height of the prism?
7
5) What is the exact surface area of the triangular prism shown below.
12
12
20
12
6) Find the total surface area and volume of the oblique cylinder. (in terms of π)
Review
1) Solve for the measure of the missing sides. Round to the tenth place.
y
12
47
x
2) Solve for the measure of the missing angle. Round to the nearest degree.
12
x
14
8