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Prisms and Cylinders

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

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**A prism is named using the name of the base.**

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**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

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

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

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

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

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

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**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.

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

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**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?

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Homework Worksheet

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**Warm Up: Find the following**

B = _____ L = _____ T = _____ V = _____ 2) P = _____ B = _____ L = _____ T = _____ V = _____

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Pyramids and Cones Surface Area

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

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**Relationships in the pyramid…**

Sits OUTSIDE the Pyramid or Cone Sits INSIDE the Pyramid or Cone

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**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

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

V = ____

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

V = ____

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

V = ____

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

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**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?

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HOMEWORK

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WARM UP

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**Volume & Surface Area of SPHERES**

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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.

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**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 =

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

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

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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)

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

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

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Homework

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Warm Up 1. Find the surface area of a square pyramid whose base is 3 m on a side and whose slant height is 5 m. 2. Find the surface area of a cone whose.

Warm Up 1. Find the surface area of a square pyramid whose base is 3 m on a side and whose slant height is 5 m. 2. Find the surface area of a cone whose.

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