Prisms and Cylinders.

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Prisms and Cylinders

Vocabulary… Lateral Faces Bases Base Edges Lateral edges Vertices Lateral Area Total Surface Area Volume

A prism is named using the name of the base.

r2 P P = C = 2πr B h L P x h T L + 2B V B x h Prism Cylinder
(perimeter of the base) add the sides of polygon P = C = 2πr B (area of base) Area formula for polygon r2 h (height of the solid) Measured from vertex ┴ the middle of the base L (lateral area) P x h T (total surface area) L + 2B V (volume) B x h

P = ____ B = ____ h = ____ L = ____ T = ____ V = ____

P = ____ B = ____ h = ____ L = ____ T = ____ V = ____

P = ____ B = ____ h = ____ L = ____ T = ____ V = ____

P = ____ B = ____ h = ____ L = ____ T = ____ V = ____

Cube with edge 8 cm. B = ____ T = ____ V = ____

A right triangular prism has lateral area 120 cm2
A right triangular prism has lateral area 120 cm2. If the base edges are 4 cm., 5 cm., and 6 cm. long, find the height of the prism.

A cube has a volume of 343 in.3. What is the total surface area of the cube?

A cylinder has a total surface area of 27π in. 2 and radius 3 inches
A cylinder has a total surface area of 27π in.2 and radius 3 inches. What is the volume of the cylinder?

Homework Worksheet

Warm Up: Find the following
B = _____ L = _____ T = _____ V = _____ 2) P = _____ B = _____ L = _____ T = _____ V = _____

Pyramids and Cones Surface Area

Vocabulary… Lateral Faces Base Base Edges Lateral edges Height Slant height Apothem of the base Lateral Area Total Surface Area

Relationships in the pyramid…
Sits OUTSIDE the Pyramid or Cone Sits INSIDE the Pyramid or Cone

L + B 1/3 B x h l ½ Pl V Pyramid Cone (slant height of face) L
(perimeter of the base) add the sides of polygon P = C = 2πr B (area of base) Area formula for polygon or circle h (height of the solid) Measured from vertex  to the middle of the base (use Pythagorean theorem if not given) l (slant height of face) Measure from the vertex  to the midpoint of the base edge (use Pythagorean theorem if not given) L (lateral area) ½ Pl T (total surface area) L + B V (Volume) 1/3 B x h

P = ____ B = ____ h = ____ l = _____ L = ____ T = ____
V = ____

P = ____ B = ____ h = ____ l = _____ L = ____ T = ____
V = ____

P = ____ B = ____ h = ____ l = _____ L = ____ T = ____
V = ____

Find the height of a triangular pyramid with a base area of 130 square meters and a volume of 650 cubic meters.

The total surface area of a cone is 27 in2. The radius is 3 in
The total surface area of a cone is 27 in2. The radius is 3 in. What is the slant height?

HOMEWORK

WARM UP

Volume & Surface Area of SPHERES

SPHERE: The set of all points in space equidistant from a given point called the center. We use the radius of the great circle to find the surface area and volume.

FORMULAS V= 4 3 𝜋 𝑟 3 SA =4𝜋 𝑟 2 VOLUME SURFACE AREA Example) Example)
Be careful and note if you’re given diameter or radius! FORMULAS VOLUME SURFACE AREA V= 4 3 𝜋 𝑟 3 Example) Radius = V = SA =4𝜋 𝑟 2 Example) Radius = SA =

Example 2 Find the volume and surface area of a sphere with radius = 6 m

Example 3 Find the volume and surface area of a sphere with diameter = 8.4 in

Example 4 Earth’s equator is about 24, 902 miles long. What is the approximate surface area of the Earth? (Earth’s Equator is a great circle that divides the Earth into two hemispheres)

Example 5 The volume of a sphere is 𝑚 3 . What is the surface area rounded to the nearest square meter?

Example 6 Find the volume of half of a grapefruit that has a circumference of 14 cm

Homework