Thus, we know that its volume is 𝑉 = 𝐵 ⋅ ℎ,  where 𝐵 is the area of the base and   c mįor cuboid B, we do not have its three dimensions, but we have the area of its base and its height. Substituting in the dimensions given in the question, we find that Therefore, we can work out its volume with 𝑉 = 𝑙 ⋅ 𝑤 ⋅ ℎ. We have the three dimensions of cuboid A We want to compare the volumes of both cuboids. Which cuboid is greater in volume? Answer Cuboid B has a base area of 2‎ ‎904 cm 2 and a We know it is given by the product of its three dimensions, but we also know that the product of two of its dimensions gives the area of one of its faces.Įxample 4: Finding the Volume of a Rectangular Prism given the Area of Its Base and Its HeightĤ0 cm, and 34 cm. Therefore, the man should use the cuboid.īefore we look at other questions, let us observe something interesting about the volume of a rectangular prism. The volume of the cubic box ( 𝑉 )  is smaller than the volume of rice, while the volume of the other box is exactly the volume needed for the rice. The second box is a cube with length 22 cm, We know that the volume of a cuboid is the product of its three dimensions (length, width, and height): 𝑉 = 𝑙 ⋅ 𝑤 ⋅ ℎ = 3 5 ⋅ 2 2 ⋅ 2 1 = 1 6 1 7 0. The first box is a cuboid of dimensions 35 cm,Ģ2 cm, and 21 cm. We need to compare the volumes of the two boxes in order to decide which one is big enough to contain 16‎ ‎170 cm 3 of rice. A box has thin walls, so we can consider that its volume is the same as its capacity. The space inside a box is called its capacity, that is, the volume of empty space inside the box that can contain something, here rice. Which box should he use? AnswerĪ box is a cuboid. He has one box which is a cuboid with dimensions of 35 cm,Īnd 21 cm and another box which is a cube with length 22 cm. 'Cuboid.Example 3: Comparing the Capacities of BoxesĪ man needs to store 16‎ ‎170 cm 3 of rice in a container. Given the diagonal, length and width find the height, volume and surface area of a rectangular prismįor more information on cuboids see: Weisstein, Eric W. Given the volume, length and width find the height, surface area, and diagonal of a rectangular prismĤ. Given the surface area, length and width find the height, volume and diagonal of a rectangular prismģ. Given the length, width and height find the volume, surface area and diagonal of a rectangular prismĢ. So you can find the volume of a cube or surface area of a cube by setting these values equal to each other. Space Diagonal of Rectangular Prism: (similar to theĪ cube is a special case where l = w = h.For example, if you are starting with mm and you know h, l and w in mm, your calculations will result with d in mm, S in mm 2 and V in mm 3. The units are in place to give an indication of the order of the results such as ft, ft 2 or ft 3. Units: Note that units are shown for convenience but do not affect the calculations. A cube is a special case where l = w = h for a rectangular prism. Enter any 3 variables for a rectangular prism into this online calculator to calculate the other 3 unknown variables.

Volume of rectangular prism