Chapter 12 & 13

Lateral and Surface Areas

& Volume

12.2 Lateral and Surface Areas of Prisms

h

L = Ph

SA = L + 2B

P = Perimeter of the base (bottom)

h

*base (shape not a rectangle)

*the height always connects the bases

B = base area

SA = 2lw + 2lh + 2wh

13.1 Volume of Prisms

h

base (bottom)

h

*base (shape not a rectangle)

B = base area

V = Bh

V = lwh

Find the lateral and surface areas of the rectangular prism.

Find the surface area of the triangular prism.

Find the lateral area of the regular hexagonal prism.

Find the surface area of the prism.

What is the volume of the prism? Round to the nearest tenth if necessary.

Find the volume of the prism.

The volume of a triangular prism is 655 cubic feet. The height of the prism is 5 feet. Find the area of one triangular base.

12.3 Lateral and Surface Area of Cylinders

r

h

L = 2πrh

S = 2πrh + 2πr2

13.1 Volume of Cylinders

r

h V = πr2h

Find the lateral area and the surface area of the cylinder. Round to the nearest tenth.

Find the lateral area and the surface area of the cylinder. Round to the nearest tenth.

Find the diameter of a base of a cylinder if the surface area is 480 square inches and the height is 8 inches.

Find the volume of the cylinder to the nearest tenth.

Find the volume of the oblique cylinder to the nearest tenth.

12.4 Lateral and Surface Areas of Pyramids

2

1

2

1

h

h

l

½ b

l Lateral edge

½ b

L = Pl

S = #sidesbl + B

2

1

l = slant height

l

13.2 Volume of Pyramids

2

1

h l V = Bh3

1

Find the lateral area and surface area of the square pyramid.

Find the surface area of the square pyramid to the nearest tenth.

Find the lateral and surface areas of the regular pyramid. Round to the nearest tenth.

Find the volume of the square pyramid.

Find the volume of the pyramid. Round to the nearest tenth if necessary.

12.5 Lateral and Surface Areas of Cones

h

r

lL = πrl

S = πrl + πr2

13.2 Volume of Cones

h

r

l V = πr2h3

1

A sugar cone has an altitude of

8 inches and a diameter of inches.

Find the lateral area of the sugar cone.

Find the surface area of the cone. Round to the nearest tenth.

Find the surface area of the cone.

Find the volume of the oblique cone to the nearest tenth.

Find the volume of the cone. Round to the nearest tenth if necessary.

12.6 Surface Area of Spheres

r

* Lateral and Surface areas are the same for a sphere

S = 4πr2

13.3 Volume of Spheres

r V = πr33

4

Find the surface area of the sphere. Round to the nearest tenth.

Find the surface area of the sphere. Round to the nearest tenth.

Find the surface area of a sphere if the circumference of the great circle is 10 feet.

Find the surface area of a sphere if the area of the great circle is approximately 220 square meters.

Find the volume of the sphere to the nearest tenth.

Find the volume a sphere with a great circle circumference of 30 centimeters. Round to the nearest tenth.

The stone spheres of Costa Rica were made by forming granodiorite boulders into spheres. One of the stone spheres has a volume of about 36,000 cubic inches. What is the diameter of the stone sphere?

12.6 Surface Area of Hemispheres

r

S = ½ 4πr2 + πr2

or

S = 3πr2

13.3 Volume of Hemispheres

r

V = ½( πr3)3

4

or

V = πr3

3

2

Find the surface area of the hemisphere.

Find the surface area of the hemisphere.

A hemisphere has a giant circle with circumference approximately 175.84 in2. What is the surface area of the hemisphere?

Find the volume of the hemisphere with a diameter of 6 feet. Round to the nearest tenth.

Find the volume of the hemisphere to the nearest tenth.