Calculer Le Volume D Un Prisme
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A prism is a solid, multisided geometric figure with two identical ends chosen bases. To find the volume of a prism, commencement calculate the area of one of the bases, and then multiply it by the height of the prism. You can cull either the superlative or the bottom base since the bases are parallel and congruent polygons, or identical 2dimensional shapes. Volume is measured in cubic units — don’t forget to add units or your instructor might dock you lot some points. Read on for stepbystep instructions for calculating the volume of five dissimilar types of prisms.

1
Write down the formula for finding the volume of a triangular prism.
The formula is simply
V = 1/2 x length ten width x height.
Even so, nosotros’ll be taking this formula apart further to use the formula
V = area of base x height.
Yous tin can find the area of the base by using the formula for finding the area of a triangle — multiplying 1/ii by the length and width of the base of operations. 
two
Find the area of the base of operations face.
To calculate the volume of a triangular prism, you lot need to kickoff find the area of the triangular base. Observe the surface area of the base of the prism by multiplying one/2 times the base of the triangle times its height. Ex: If the acme of the triangular base is 5 cm and the base of operations of the triangular prism is 4 cm, so the surface area of the base is 1/two 10 5 cm x four cm, which is 10 cm^{2}.
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3
Find the elevation.
Let’south say the height of this triangular prism is 7 cm. 
four
Multiply the area of the triangular base face times the height.
But multiply the area of the base times the superlative. After you multiply the base and height, you’ll accept the volume of the triangular prism. Ex:ten cm^{2}
x 7 cm = seventy cm^{3}
 Ex:ten cm^{2}

5
State your answer in cubic units.
You should always apply cubic units when you’re calculating volume because you’re working with three dimensional objects. The concluding reply is 70 cm.^{3}
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one
Write down the formula for finding the book of a cube.
The formula is only
V = side^{3}.
A cube is a prism that happens to have three equal sides.^{[i] } 
two
Find the length of 1 side of the cube.
All of the sides are equal, then information technology doesn’t matter which side yous cull. Ex: Length = 3 cm.

iii
Cube information technology.
To cube a number, simply multiply it by itself twice. The cube of “a” is “a ten a ten a,” for case. Since all of the lengths of the sides of the cube are equal, you don’t accept to observe the expanse of the base and multiply it by the height and and then multiply it by the length. Multiplying any two sides of the cube will give yous the area of the base, and any tertiary side could represent the pinnacle. You can still think of this as multiplying the length, width, and superlative when they all just happen to be the same. Ex: iii cm^{3}
= 3 cm. * 3 cm. * 3 cm. = 27 cm.^{3}
 Ex: iii cm^{3}

iv
State your answer in cubic units.
Don’t forget to put your final answer in cubic units. The concluding respond is 27 cm.^{three}
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1
Write downwards the formula for finding the volume of a rectangular prism.
The formula is only
V = length * width * acme.
A rectangular prism is a prism with a rectangular base of operations. 
two
Observe the length.
The length is the longest side of the apartment surface of the rectangle on the top or bottom of the rectangular prism. Ex: Length = 10 cm.

3
Find the width.
The width of the rectangular prism is the shorter side of the flat surface of the rectangle on the meridian or bottom of the shape. Ex: Width = in 8 cm.

four
Find the acme.
The height is the part of the rectangular prism that rises upwardly. You can imagine the height of the rectangular prism as the function that stretches upwardly a flat rectangle and makes it threedimensional. Ex: Height = 5 cm.

5
Multiply the length, the width, and the height.
Y’all can multiply them in whatsoever order to go the same result. Using this method, you have substantially found the expanse of the rectangular base of operations ( 10 x eight) and then have multiplied it by its height, 5. But to detect the volume of this prism, yous tin can multiply the lengths of the sides in whatsoever order. Ex: 10 cm. * 8 cm. * five cm = 400 cm.^{3}

half dozen
State your answer in cubic units.
The final answer is 400 cm.^{three}
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1
Write downwardly the formula for calculating the volume of a trapezoidal prism.
The formula is:
Five = [1/two x (base_{ane}
+ base_{ii}) 10 height] x elevation of the prism.
You should use the offset part of this formula to discover the area of the trapezoidal base of operations of the prism before y’all move forward.^{[2] } 
2
Discover the surface area of the trapezoidal base face.
To exercise this, simply plug the two bases and the peak of the trapezoidal base into the formula. Let’due south say base of operations ane = viii cm, base of operations ii = vi cm, and height = x cm.
 Ex: 1/2 x (6 + 8) 10 10 = 1/2 x xiv cm x 10 cm = 70 cm^{2}.

three
Discover the height of the trapezoidal prism.
Allow’s say the peak of the trapezoidal prism is 12 cm. 
four
Multiply the area of the base of operations face times the height.
To summate the volume of the trapezoidal prism, simply multiply the area of the base times the pinnacle. lxx cm^{ii}
x 12 cm = 840 cm^{3}.
 lxx cm^{ii}

5
State your answer in cubic units.
The final answer is 840 cm^{3}
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1
Write the formula for finding the volume of a regular pentagonal prism.
The formula is
V = [1/2 ten 5 x side x apothem] x peak of the prism.
You can use the first part of the formula to notice the expanse of the pentagonal base face. You can recollect of this every bit finding the area of the five triangles that make upwardly a regular polygon. The side is simply the width of one triangle, and the apothem is the height of one of the triangles. You’ll be multiplying by one/2 because that’south function of finding the expanse of a triangle and and so multiplying this by 5 because 5 triangles brand up the pentagon.^{[3] } For more than data on finding the apothem if one is non provided for you, look here.^{[4] }

2
Observe the expanse of the pentagonal base face.
Permit’due south say the length of a side is half dozen cm and the length of the apothem is 7 cm. Simply plug these numbers into the formula: A = 1/2 x 5 x side x apothem
 A = one/ii 10 five x 6 cm x vii cm = 105 cm^{ii}

three
Find the height.
Let’southward say the height of the shape is 10 cm. 
4
Multiply the area of the pentagonal base confront times the height.
Just multiply the expanse of the pentagonal base, 105 cm^{two}, times the height, ten cm, to discover the volume of the regular pentagonal prism. 105 cm^{2}
10 x cm = 1050 cm^{3}
 105 cm^{2}

five
State your answer in cubic units.
The final answer is 1050 cm^{3}.
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Add New Question

Question
How do I find the volume of rectangular prisms?
Calculate the area of the base (length multiplied by width), then multiply past the elevation.

Question
How do I calculate the volume of a rectangular prism if there are two unlike heights?
A rectangular prism would non have ii different heights. If yous’re asking about a notrectangular prism, the volume formula would involve finding the average height of some of the sides.

Question
How do I find the volume of a circular prism?
The volume of a cylinder is found by squaring the radius and then multiplying by the product of pi and the pinnacle of the cylinder. (5 = πr²h.)
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Video

Try not to misfile “base of operations” with “base of operations face”. Base face refers to the twodimensional shape which forms the base of the entire prism (usually, its top and bottom). But that base face may have its own base of operations — a onedimensional length along an edge which serves as the base measurement when finding the area of the 2dimensional shape.
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Article Summary
10
To detect the volume of a triangular prism, use the equation V = ½ × length × width × height, or V = the surface area of the base × the peak. Find the area of the base by multiplying ½ × the length and width of one of the triangular bases of the prism. Then, locate the height, and multiply the meridian by the expanse of the base. For case, a triangular prism with a length of 4 cm and a width of 5 cm would accept an area of x cm^two. If the height was vii cm, the volume of the prism would be 70 cm cubed.
If yous desire to learn how to observe the volume of a rectangular or pentagonal prism, keep reading the article!
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Calculer Le Volume D Un Prisme
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