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**Volume of Prisms & Cylinders**

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Definitions A prism is a three-dimensional figure named for the shape of its bases. The two bases are congruent polygons. All of the other faces are parallelograms.

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**Every prism is named by its BASE.**

Triangular prism Height Base

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**If all six faces of a rectangular prism are squares, it is a cube.**

Remember!

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**Definition of a Cylinder**

A cylinder is made up of two identical circular bases and one rectangle.

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**Definition of a Cylinder continued…**

The BASE of a cylinder is the circle at the top or at the bottom. Height The HEIGHT is the distance between the two circular bases. Base

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How to Find Volume Volume of all prisms and cylinders is found by multiplying the area of the base times the height. Step 1: Decide what shape the base is. (rectangle, triangle or circle) Step 2: Find the area of the base. Step 3: Multiply by height.

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**Find the volume of the rectangular prism**

Step 1: Determine what shape the base is: Rectangle Step 2: Find the area of the base (8.5)(5) = Step 3: Multiply by the height: 42.5(6) = 42.5 6 in. 255 in3 5 in. 8.5 in.

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**Find the volume of the triangular prism**

Step 1: Determine what shape the base is: Triangle Step 2: Find the area of the base ½ (12)(10) = Step 3: Multiply by the height: 60(14)= 14 ft 60 12 ft To find the area of a triangle multiply ½(base)(height) 840 ft 3 10 ft 12 ft

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**Find the volume of the cylinder.**

Step 1: Determine what shape the base is: circle Step 2: Find the area of the base p (52) = Step 3: Multiply by the height: 25 p(15)= 15 in. 25p 375p in3 Area of a circle is found by multiplying p by radius squared. Radius = 5 in!

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**Steps for finding Volume:**

Find the area of the base. Multiply by height. All units used are cubed (3)

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