Now that we have learned how to work out the volume of a rectangular prism when either We find that 𝑉 is greater than 𝑉 , which means that cuboid B is greater in volume than cuboid A. Substituting in the values given in the question, we find that 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. Example 3: Comparing the Capacities of BoxesĪ man needs to store 16 170 cm 3 of rice in a container.
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