What were we doing in 3D? Geometry Mathematical Reflection 3D.

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Presentation transcript:

What were we doing in 3D? Geometry Mathematical Reflection 3D

In this investigation, O You found lateral surface area and total surface area of solids by visualizing their nets. O You also used formulas to calculate volumes.

Habits and Skills You developed these habits and skills: O Visualize a net for a three-dimensional object. O Understand surface area and volume. O Reason by continuity to connect formulas.

DHoM O Visualize O Generalize O Make and verify a conjecture

Vocabulary and Notation O Apex O Base O Circumference O Cone O Cylinder O Face O Frustum O Lateral face O Lateral surface O Lateral surface area O Oblique prism O Oblique pyramid O Perimeter O Polyhedron O Pyramid O Right pyramid O Slant height O Surface area O Volume

Big Idea The shape of lateral faces of O right prisms are rectangles. O right pyramids are triangles. O Total surface areas are the areas of all faces O Volume is the number of cubes that you can fit in a space.

Lateral Surface Area O The area of all faces except bases

Pyramids

Slant height and height O Height is the distance from apex to the base O Slant height is the height of the face

Cylinder

Lateral surface area (LA)

Cones

The simplified formulas for LA

Volumes of Solids

Discussion Question How can you use perimeter and area of two- dimensional shapes to find surface area and volume of three- dimensional solids? For prisms, and cylinders, use the product of the height of the solid and the perimeter of the base to calculate the lateral area. Add the areas of the bases to the product to calculate total surface area.

Discussion Question What is the relationship between a prism and a cylinder? Between a pyramid and a cone? A regular prism with a very large number of sides resembles a cylinder. A regular pyramid with a very large number of sides resembles a cone.

Problem 1 O A cylinder and a cone have the same base. The height of each is equal to the radius of its base. What is the ratio of their lateral surface areas?

Problem 2 Draw a net for the regular tetrahedron shown below.

Problem 3 What is the total surface area of a cylinder with diameter 108 cm and height 18cm?

Problem 4 Two cones have slant height 8 in. The first cone has a radius of 4 in. The second cone has a diameter of 12 in. What is the ratio of their lateral surface areas?

Problem 5 Stephanie has a goldfish who lives in a tank like the one shown at the right. The cone juts up into the tank to give the fish something to swim around. How much water does Stephanie need to fill the tank? (Disregard the volume of the fish.)

Are you ready for 4A? In 4A, you will learn how to O Approximate the scale factor relating two pictures by measuring O Use a given scale factor to interpret a map or blueprint O Decide whether two figures are well-scaled copies of each other Don’t forget HOMEWORK!!