Volume of Prisms and Cylinders Measured in cubic

  • Slides: 14
Download presentation
Volume of Prisms and Cylinders Measured in cubic units 3

Volume of Prisms and Cylinders Measured in cubic units 3

Volumes of Prisms and Cylinders A prism is a threedimensional figure named for the

Volumes of Prisms and Cylinders A prism is a threedimensional figure named for the shape of its bases. Triangular prism has triangles for bases. Rectangular prism has rectangles for bases. If all six faces of a prism are squares, it is a cube.

Triangular prism In this triangular prism the two bases are triangles. The formula for

Triangular prism In this triangular prism the two bases are triangles. The formula for volume of a triangular prism is V = Bh, where B is area of the base and h is height.

Rectangular prism In this rectangular prism the two bases are rectangles. The volume formula

Rectangular prism In this rectangular prism the two bases are rectangles. The volume formula is V = Bh V = (lw)h length · width · height

CUBE Here is a 3 -dimensional view of a cube. The view on the

CUBE Here is a 3 -dimensional view of a cube. The view on the left is the cube. The view on the right shows the base of the cube. The formula for the volume of a cube: V = Bh V = lwh

Cylinder: a cylinder is a three-dimensional figure with two circular bases. The volume of

Cylinder: a cylinder is a three-dimensional figure with two circular bases. The volume of a cylinder is the area of the base B times the height h. V = Bh or V = (πr²)h

Volumes of Pyramids and Cones 1/3 of prisms and cylinders

Volumes of Pyramids and Cones 1/3 of prisms and cylinders

A pyramid is named for the shape of its base. The base is a

A pyramid is named for the shape of its base. The base is a polygon, and all the other faces are triangles. A cone has a circular base. The height of a pyramid or cone is a perpendicular line measured from the highest point to the base.

A cone has a circular base. The height of a pyramid or cone is

A cone has a circular base. The height of a pyramid or cone is perpendicular line measured from the highest point to the base. In the cone to the left the height is h and the radius of the circular base is r. The s is the slant height which is used to measure surface area of a cone or pyramid. The volume formula for a cone is V = 1/3 Bh or V = 1/3πr²h

A pyramid is named for its base. The base is a polygon, and all

A pyramid is named for its base. The base is a polygon, and all the other faces are triangles that meet at a common vertex. The height is a perpendicular line from the base to the highest point. The volume formula for a pyramid is V = 1/3 Bh V = 1/3(lw)h

The volumes of cones and pyramids are related to the volumes of cylinders and

The volumes of cones and pyramids are related to the volumes of cylinders and prisms. V = πr²h V = Bh V = 1/3πr²h V = 1/3 Bh A cone is 1/3 the size of a cylinder with the same base and height. Also, a pyramid is 1/3 the size of a prism with the same height and base.

Surface Area of Prisms and Cylinders Back to areas 2 again

Surface Area of Prisms and Cylinders Back to areas 2 again

Surface area of objects are used to advertise, inform, create art, and many other

Surface area of objects are used to advertise, inform, create art, and many other things. On the left is an anamorphic image, which is a distorted picture that becomes recognizable when reflected onto a cylindrical mirror.

When you flatten-out a three-dimensional object the diagram is called a net. Which of

When you flatten-out a three-dimensional object the diagram is called a net. Which of the following answers is the correct net for the cube. Choose a, b, c, or d.