what is the formula to the volume of a prism

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A prism is a solid, multi-sided geometric effigy with ii identical ends called bases. To find the volume of a prism, starting time calculate the expanse of one of the bases, and so multiply it by the summit of the prism. You can choose either the superlative or the bottom base of operations since the bases are parallel and congruent polygons, or identical 2-dimensional shapes. Volume is measured in cubic units — don't forget to add units or your teacher might dock you some points. Read on for step-by-step instructions for calculating the book of 5 different types of prisms.

1. 1

   Write downwardly the formula for finding the book of a triangular prism. The formula is only V = 1/2 x length x width ten superlative. Nonetheless, nosotros'll be taking this formula apart farther to utilize the formula V = surface area of base x height. You can observe 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.

2. two

   Detect the area of the base face. To summate the volume of a triangular prism, you need to starting time find the surface area of the triangular base. Discover the expanse of the base of the prism by multiplying ane/2 times the base of operations of the triangle times its summit.

   • Ex: If the height of the triangular base is v cm and the base of the triangular prism is 4 cm, so the expanse of the base is 1/ii 10 5 cm 10 iv cm, which is ten cm^two.

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3. three

   Detect the elevation. Permit's say the elevation of this triangular prism is 7 cm.

4. 4

   Multiply the expanse of the triangular base face times the height. Simply multiply the surface area of the base times the pinnacle. Later you lot multiply the base and height, you'll have the book of the triangular prism.

   • Ex:10 cm² ten 7 cm = 70 cmⁱⁱⁱ

5. v

   State your answer in cubic units. You should e'er apply cubic units when you're calculating volume because you're working with iii dimensional objects. The last answer is lxx cm.^three

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1. i

   Write downwards the formula for finding the book of a cube. The formula is simply V = side³. A cube is a prism that happens to have three equal sides.^[1]

2. 2

   Find the length of one side of the cube. All of the sides are equal, so it doesn't matter which side you choose.

   • Ex: Length = 3 cm.

3. 3

   Cube it. To cube a number, only multiply information technology by itself twice. The cube of "a" is "a ten a x a," for example. Since all of the lengths of the sides of the cube are equal, you don't have to find the area of the base and multiply information technology by the peak and then multiply it past the length. Multiplying any two sides of the cube will give you lot the area of the base, and any third side could represent the summit. You can notwithstanding remember of this every bit multiplying the length, width, and superlative when they all just happen to be the same.

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

4. 4

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

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1. one

   Write downwards the formula for finding the volume of a rectangular prism. The formula is simply V = length * width * height. A rectangular prism is a prism with a rectangular base.

2. 2

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

   • Ex: Length = x cm.

3. 3

   Discover the width. The width of the rectangular prism is the shorter side of the flat surface of the rectangle on the top or bottom of the shape.

   • Ex: Width = in 8 cm.

4. 4

   Find the height. The acme is the office of the rectangular prism that rises up. You can imagine the summit of the rectangular prism equally the part that stretches upwardly a flat rectangle and makes it three-dimensional.

   • Ex: Height = 5 cm.

5. 5

   Multiply the length, the width, and the height. You can multiply them in any society to get the same result. Using this method, you lot accept essentially constitute the surface area of the rectangular base ( x 10 8) and so have multiplied information technology by its top, 5. Only to find the volume of this prism, you lot can multiply the lengths of the sides in whatsoever order.

   • Ex: x cm. * 8 cm. * 5 cm = 400 cm.³

6. 6

   Country your reply in cubic units. The final answer is 400 cm.^three

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1. one

   Write down the formula for calculating the volume of a trapezoidal prism. The formula is: V = [1/2 x (base_ane + base₂) x height] x height of the prism. You should use the commencement part of this formula to find the area of the trapezoidal base of the prism before you movement forward.^[ii]

2. 2

   Discover the area of the trapezoidal base face. To exercise this, simply plug the two bases and the superlative of the trapezoidal base into the formula.

   • Let'south say base 1 = viii cm, base 2 = 6 cm, and height = x cm.
   • Ex: ane/ii ten (6 + 8) x 10 = ane/ii x 14 cm x 10 cm = 70 cmⁱⁱ.

3. 3

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

4. iv

   Multiply the surface area of the base of operations face times the height. To calculate the volume of the trapezoidal prism, but multiply the area of the base times the acme.

   • 70 cm² x 12 cm = 840 cmⁱⁱⁱ.

5. v

   State your answer in cubic units. The final answer is 840 cm³

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1. ane

   Write the formula for finding the volume of a regular pentagonal prism. The formula is Five = [1/2 x v x side x apothem] x height of the prism. You lot can use the first part of the formula to detect the area of the pentagonal base of operations face. You can remember of this as finding the area of the five triangles that make up a regular polygon. The side is simply the width of one triangle, and the apothem is the height of one of the triangles. Y'all'll be multiplying by 1/2 considering that'south part of finding the expanse of a triangle and then multiplying this by 5 because 5 triangles make upwardly the pentagon.^[3]

   • For more than information on finding the apothem if one is not provided for you, look here.^[4]

2. 2

   Find the area of the pentagonal base face. Permit's say the length of a side is half dozen cm and the length of the apothem is vii cm. Just plug these numbers into the formula:

   • A = 1/2 10 v x side x apothem
   • A = 1/two 10 5 10 vi cm x 7 cm = 105 cm²

3. 3

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

4. 4

   Multiply the area of the pentagonal base confront times the height. Only multiply the expanse of the pentagonal base, 105 cm², times the summit, 10 cm, to detect the volume of the regular pentagonal prism.

   • 105 cm² 10 10 cm = 1050 cm³

5. 5

   Country your answer in cubic units. The last answer is 1050 cm³.

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Add New Question

• Question

  How practise I notice the volume of rectangular prisms?

  

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

• Question

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

  

  A rectangular prism would not have two different heights. If y'all're asking about a non-rectangular prism, the volume formula would involve finding the boilerplate summit of some of the sides.

• Question

  How do I find the volume of a round prism?

  

  The volume of a cylinder is plant past squaring the radius and and so multiplying past the production of pi and the superlative of the cylinder. (V = πr²h.)

• Question

  How practice I find the volume of a prism?

  

  Every bit with any right prism, you summate the area of the base of operations and and then multiply by the elevation.

• Question

  How to find the book of a rectangular box without knowing the acme?

  

  That's non possible, unless you're given some clue to figure out the top.

• Question

  How exercise I detect the volume of a hexagonal prism?

• Question

  How do I find the volume of a rhombic prism?

  

  Multiply the expanse of the base by the height.

• Question

  What is the book of a rectangular pyramid?

  

  The volume is one-third of the product of the length, width, and height. Put another way, it's the surface area of the base, multiplied past the superlative and divided by 3.

• Question

  How do I detect the volume of a diamond prism?

  

  Multiply the area of the diamond by the peak of the prism.

• Question

  How practice I find the book of a heptagonal prism (a seven-sided 3D shape)?

  

  Multiply the expanse of the base of operations past the summit. To find the area, see [[Discover the Expanse of Regular Polygons]].

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• Attempt not to misfile "base of operations" with "base face up". Base face refers to the 2-dimensional shape which forms the base of the entire prism (usually, its elevation and bottom). Only that base of operations face may have its own base --- a i-dimensional length along an edge which serves equally the base of operations measurement when finding the area of the two-dimensional shape.

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Article Summary X

To find the volume of a triangular prism, apply the equation V = ½ × length × width × pinnacle, or V = the area of the base of operations × the height. Find the expanse of the base by multiplying ½ × the length and width of one of the triangular bases of the prism. And then, locate the height, and multiply the height by the area of the base. For case, a triangular prism with a length of 4 cm and a width of 5 cm would have an area of 10 cm^2. If the height was 7 cm, the volume of the prism would be 70 cm cubed. If you want to learn how to observe the volume of a rectangular or pentagonal prism, keep reading the article!

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