Drag and drop an answer to each box to correctly explain the derivation of the formula for the volume of a pyramid.
2 answers:
The volume of a prism is its base area times its height. If we compare this to the formula of the pyramid,we will see one is exactly a third of the other. This means that the volume of a pyramid is exactly one third the volume of the prism with the same base and height.
The volume of a pyramid is one-third the volume of a prism with the same base and height because the formula for volume of prism is V=B.h.where B is area of base and h is height.The formula for volume of pyramid is
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Answer:
BA = 25π,
LA = 25√2π,
TA = 25π + 25√2π,
V = 41 and 2 / 3π
Step-by-step explanation:
We need to determine the height here, as it is not given, and is quite important to us. The height is a perpendicular line segment to the radius, hence forming a 45 - 45 - 90 degree triangle as you can see. Therefore, by " Converse to Base Angles Theorem " the height should be equal in length to the radius,
( Height = 5 inches = Radius
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Now knowing the height, let's begin by calculating the base area. By it's name, we have to find the area of the base. As it is a circle, let us apply the formula " πr^2 "
- Base Area = 25π
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The lateral area is simply the surface area excluding the base area, the surface area having a formula of " πr^2 + πrl. " Thus, the lateral area can be calculated through the formula " πrl, " but as we are not given the slant height ( l ) we have to use another formula, -
- Lateral Area = 25√2π
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And the surface area is the base area + lateral area -
- Surface Area
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The volume of a cone is 1 / 3rd that of a cylinder, with a simple formula of Base * height. Therefore, we can conclude the following -
- Volume = 41 and 2 / 3π