Question

Match the following.

Answer 1

Answers:

1. Pyramid
2. Rectangular Prism
3. Cylinder
4. Cone
5. Triangular Prism

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Explanation:

1. The formula for the volume of a pyramid is (1/3)*B*h, where B is the area of the base. If we're dealing with a rectangular pyramid, like those found in Egypt, then the area of the base is B = length*width.
2. The volume for a prism is found by multiplying length (L), width (W), and height (H). So V = LWH. Think of having a 2 by 3 rectangle of blocks. We would have 2*3 = 6 blocks in total. Then if we have 5 layers of these stacked then we have 2*3*5 = 6*5 = 30 blocks in total. This is one way to visualize how the volume formula works.
3. To get the volume of a cylinder, we multiply the area of the base (pi*r^2) by the height (h). So that's where pi*r^2*h comes from.
4. The volume of a cone is 1/3 that of a cylinder's volume. This is when the cone and cylinder have the same radius, and also the same height. It's not required that r = h.
5. Since all of the other answer choices are used up, the only thing left is "triangular prism". It's strongly implied here that B is the area of the triangular base. Though the formula Bh applies to any prism and it doesn't have to be a triangular prism. Note how B = LW, so Bh is the same as LWH, meaning that a rectangular prism can use the Bh formula.