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How To Find The Volume Of An Octagonal Prism

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A prism is a solid, multi-sided geometric figure with two identical ends called bases. To find the volume of a prism, starting time summate the area of 1 of the bases, then multiply information technology by the peak of the prism. Y'all tin cull either the top or the bottom base since the bases are parallel and congruent polygons, or identical 2-dimensional shapes. Book is measured in cubic units — don't forget to add units or your teacher might dock y'all some points. Read on for step-by-pace instructions for calculating the book of five different types of prisms.

  1. 1

    Write down the formula for finding the volume of a triangular prism. The formula is merely V = ane/2 ten length x width x height. Yet, we'll exist taking this formula apart farther to use the formula V = area of base x height. You can find the area of the base by using the formula for finding the surface area of a triangle -- multiplying 1/2 by the length and width of the base.[1]

  2. 2

    Find the expanse of the base face up. To calculate the book of a triangular prism, you need to first find the area of the triangular base. Find the area of the base of the prism by multiplying ane/2 times the base of the triangle times its height.[2]

    • Ex: If the acme of the triangular base is 5 cm and the base of the triangular prism is 4 cm, then the expanse of the base is 1/2 x 5 cm 10 4 cm, which is 10 cm2.

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  3. three

    Detect the height. Let's say the meridian of this triangular prism is 7 cm.

  4. 4

    Multiply the area of the triangular base face times the height. Simply multiply the expanse of the base times the height. After you lot multiply the base and elevation, you'll take the book of the triangular prism.[3]

    • Ex:10 cm2 x seven cm = 70 cm3

  5. 5

    State your answer in cubic units. Yous should e'er utilise cubic units when yous're calculating book because you're working with iii dimensional objects. The final answer is 70 cm.3

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  1. ane

    Write down the formula for finding the book of a cube. The formula is simply V = sidethree. A cube is a prism that happens to accept three equal sides.[4]

  2. 2

    Find the length of one side of the cube. All of the sides are equal, and then it doesn't affair which side you cull.

    • Ex: Length = iii cm.

  3. 3

    Cube it. To cube a number, only multiply it past itself twice. The cube of "a" is "a 10 a x a," for case. Since all of the lengths of the sides of the cube are equal, you don't accept to find the area of the base of operations and multiply it by the elevation and and so multiply it past the length. Multiplying whatever two sides of the cube volition give you the area of the base, and any third side could represent the height. You lot tin can still recall of this as multiplying the length, width, and height when they all simply happen to exist the aforementioned.[5]

    • Ex: three cmiii = iii cm. * iii cm. * 3 cm. = 27 cm.3

  4. 4

    State your answer in cubic units. Don't forget to put your final respond in cubic units. The final respond is 27 cm.3

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  1. 1

    Write downwardly the formula for finding the book of a rectangular prism. The formula is only V = length * width * height. A rectangular prism is a prism with a rectangular base.[6]

  2. 2

    Find the length. The length is the longest side of the apartment surface of the rectangle on the top or lesser of the rectangular prism.

    • Ex: Length = ten cm.

  3. 3

    Find the width. The width of the rectangular prism is the shorter side of the flat surface of the rectangle on the height or lesser of the shape.

    • Ex: Width = in 8 cm.

  4. 4

    Find the tiptop. The peak is the office of the rectangular prism that rises up. You can imagine the height of the rectangular prism equally the role that stretches upwards a apartment rectangle and makes it three-dimensional.

    • Ex: Height = v cm.

  5. v

    Multiply the length, the width, and the height. You tin multiply them in any order to become the same result. Using this method, you have essentially institute the area of the rectangular base ( 10 x eight) and then have multiplied information technology by its superlative, 5. Just to notice the volume of this prism, you tin can multiply the lengths of the sides in whatever order.[7]

    • Ex: 10 cm. * viii cm. * 5 cm = 400 cm.3

  6. vi

    State your answer in cubic units. [8] The final answer is 400 cm.3

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  1. 1

    Write downwardly the formula for calculating the volume of a trapezoidal prism. The formula is: V = [1/two x (base1 + base2) x height] x summit of the prism. You should use the showtime part of this formula to observe the area of the trapezoidal base of operations of the prism before you movement forrad.[9]

  2. two

    Find the area of the trapezoidal base of operations face. To do this, simply plug the two bases and the height of the trapezoidal base into the formula.

    • Let'south say base 1 = 8 cm, base of operations 2 = 6 cm, and height = x cm.
    • Ex: i/2 10 (6 + 8) ten 10 = one/2 x xiv cm x x cm = 70 cm2.

  3. three

    Find the height of the trapezoidal prism. Let'south say the meridian of the trapezoidal prism is 12 cm.

  4. 4

    Multiply the area of the base face times the height. To calculate the volume of the trapezoidal prism, just multiply the area of the base times the pinnacle.[10]

    • 70 cm2 x 12 cm = 840 cm3.

  5. 5

    State your respond in cubic units. The final reply is 840 cm3

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  1. 1

    Write the formula for finding the volume of a regular pentagonal prism. The formula is V = [1/2 x five x side ten apothem] x top of the prism. You tin can use the first office of the formula to find the area of the pentagonal base face. You lot can retrieve of this equally finding the area of the five triangles that make upward a regular polygon. The side is simply the width of one triangle, and the apothem is the elevation of one of the triangles. You'll be multiplying past i/2 because that'southward part of finding the surface area of a triangle and and then multiplying this past v because 5 triangles make upward the pentagon.[eleven]

    • For more information on finding the apothem if one is not provided for you, look here.[12]

  2. ii

    Notice the surface area of the pentagonal base of operations face. Let'due south say the length of a side is half dozen cm and the length of the apothem is 7 cm. Just plug these numbers into the formula:

    • A = ane/ii ten 5 x side x apothem
    • A = i/2 x five x 6 cm x 7 cm = 105 cmii

  3. 3

    Find the height. Let's say the height of the shape is x cm.

  4. 4

    Multiply the area of the pentagonal base face times the height. Only multiply the area of the pentagonal base, 105 cm2, times the height, 10 cm, to find the volume of the regular pentagonal prism.[xiii]

    • 105 cm2 x 10 cm = 1050 cm3

  5. 5

    State your reply in cubic units. The concluding answer is 1050 cm3.

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Add together New Question

  • Question

    How do I detect the volume of rectangular prisms?

    Donagan

    Calculate the area of the base of operations (length multiplied past width), and so multiply by the height.

  • Question

    How practice I calculate the volume of a rectangular prism if there are two different heights?

    Donagan

    A rectangular prism would not have two different heights. If you're request near a not-rectangular prism, the volume formula would involve finding the boilerplate height of some of the sides.

  • Question

    How practise I discover the volume of a circular prism?

    Donagan

    The volume of a cylinder is institute by squaring the radius and and so multiplying past the product of pi and the height of the cylinder. (V = πr²h.)

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  • Try not to confuse "base" with "base face up". Base confront refers to the 2-dimensional shape which forms the base of operations of the entire prism (commonly, its elevation and bottom). But that base face may have its own base of operations --- a 1-dimensional length along an edge which serves as the base measurement when finding the area of the 2-dimensional shape.

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Article Summary 10

To detect the volume of a triangular prism, use the equation 5 = ½ × length × width × superlative, or V = the area of the base × the pinnacle. Detect the area of the base of operations by multiplying ½ × the length and width of 1 of the triangular bases of the prism. Then, locate the height, and multiply the tiptop by the area of the base. For example, a triangular prism with a length of 4 cm and a width of 5 cm would take an area of x cm^2. If the height was 7 cm, the volume of the prism would be 70 cm cubed. If yous desire to learn how to discover the volume of a rectangular or pentagonal prism, keep reading the article!

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Source: https://www.wikihow.com/Calculate-the-Volume-of-a-Prism

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