Video transcriptWhat is the volume of this box? Drag on the box to rotate it. So this is pretty neat. We can actually sit and rotate this box. And here it looks like everything's being measured in meters. So we want to measure our volume in terms of cubic meters. That's going to be our unit cube here. So when we want to think about how many cubic meters could fit in this box, we've already seen examples. You really just have to multiply the three different dimensions of this box. So if you wanted the number of cubic meters that could fit in here, it's going to be six meters times 8 meters times 7 meters which is going to give you something in cubic meters. So let's think about what that is. 6 times 8 is 48. Let me see if I can do this in my head. 48 times 7, that's 40 times 7, which is going to be 280 plus 8 times 7, which is 56, 280 plus 56 is going to be 336. Let's check our answer. Let's do one more of these. So what's the volume of this box? We'll once again, we have its height at six feet. Now everything is being measured in feet. We have it's width being four feet. So we could multiple the height times the width of four feet. And then we can multiply that times its depth of two feet. So 6 times 4 is 24 times 2 is 48 feet. 48, and I should say cubic feet. We're saying how many cubic feet can fit in here? When we multiply the various dimensions measured in feet, we're counting almost how many of those cubic feet can fit into this box. Show
If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. A prism is a polyhedron in which all the faces are flat, and the bases are parallel to each other. It is a solid object with flat faces, identical ends, and the same cross-section along with its length. In Geometry, we will learn the different types of prisms, such as triangular prism, pentagonal prism, and hexagonal prism. Since it is a three-dimensional shape, a prism has a surface area and volume. In this article, we are going to discuss the volume of a prism, its formulas and solved problems. What is the Volume of a Prism?The volume of a prism is defined as the total space occupied by the three-dimensional object. Mathematically, it is defined as the product of the area of the base and the length. Therefore, The volume of a Prism = Base Area × Length The measurement unit used to represent the volume of a three-dimensional object is cubic units. Volume of a Prism FormulaNow, let us discuss the volume of the different prism formulas, such as the volume of the triangular prism, rectangular prism, pentagonal prism, and so on. Volume of a Triangular Prism A triangular prism is a prism that has three rectangular faces and two triangular bases. Since the cross-section of the triangular prism is a triangle, the formula for the volume of a triangular prism is given as: The volume of a Triangular Prism = (½) abh cubic units. Where a = Apothem length of a triangular prism b = Base length of a triangular prism h = height of a triangular prism Volume of a Rectangular prismA rectangular prism has four rectangular faces and two parallel rectangular bases. We know that the cross-section of a rectangular prism is a rectangle. The rectangular prism is also known as a “Cuboid”. Hence, the formula to find the volume of a rectangular prism is given: The volume of a Rectangular Prism = l.b.h cubic units. Where l = Base width of a rectangular prism b = Base length of a rectangular prism h = height of a rectangular prism Volume of a Pentagonal PrismA pentagonal prism has five rectangular faces and two parallel pentagonal bases. Since the base area of the pentagonal prism is (5/2) ab, the volume of the pentagonal prism is given as: The Volume of a Pentagonal Prism = (5/2) a.b.h cubic units Where, a – Apothem length of the pentagonal prism. b – Base length of the pentagonal prism. h – Height of the pentagonal prism Volume of a Hexagonal PrismA hexagonal prism is a prism with six rectangular faces and two parallel hexagonal bases. The base area of the hexagonal prism is 3ab, the formula to find the volume of a hexagonal prism is given as: The volume of a Hexagonal Prism = 3abh cubic units Where a – Apothem length of the hexagonal prism. b – Base length of the hexagonal prism. h – Height of the hexagonal prism. Volume of a Prism ExampleQuestion 1: What is the volume of a triangular prism with dimensions of 12 m, 16 m and 20 m as given in figure. Solution: The volume of a triangular prism can be found by V = Area of base × Height of Prism As the base is triangular, so, Area of triangle = ½ × base × height = ½ × base × height =½ × 12 × 16 = 96 So, Volume of prism = 96 × 20 = 1920 cubic meter. Frequently Asked Questions – FAQsThe
volume of a Prism = Base Area × Length The volume of a Triangular Prism = (½) abh cubic units. The volume of a Rectangular Prism = lbh cubic units. The Volume of a Pentagonal Prism = (5/2) abh cubic units The volume of a Hexagonal Prism = 3abh cubic units To learn more formulas, register with BYJU’S – The Learning App and download the app to practice more problems. How do you find the volume of prism?To find the volume of a rectangular prism, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units.
What are the two formulas for volume of a prism?Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
What are the formulas for volume?Whereas the basic formula for the area of a rectangular shape is length × width, the basic formula for volume is length × width × height. How you refer to the different dimensions does not change the calculation: you may, for example, use 'depth' instead of 'height'.
What is volume of a prism in math?The volume of a prism is defined as the total space occupied by the three-dimensional object. Mathematically, it is defined as the product of the area of the base and the length. Therefore, The volume of a Prism = Base Area × Length.
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What is the formula for volume of a prism
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