A solid right pyramid has a square base with an edge length of x cm and a height of y cm. Which expression represents the volume
2 answers:
The <em><u>correct answer</u></em> is:
Explanation:
The volume of a right rectangular prism is found by finding the area of the base and multiplying by the height. This is because there are "layers" of the base from the bottom to the top, making the height the number of "layers."
However, in a pyramid, the shape comes to a point. This makes the volume of a pyramid 1/3 of that of the corresponding prism.
For our pyramid, the area of the base would be x(x) = x². There are y layers of this base, so this would be x²y. Since it is a pyramid, this gives us (1/3)x²y.
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If we write the first integer as the variable n, all numbers that come after it can be written as n+1, n+2, etc.
so the sum of four consecutive integers is:
sum = n + (n+1) + (n+2) + (n+3)
if we simplify:
sum = 4n +6
and if we want to know what the first integer is, we can re-write the equation as:
= n
and that is your answer.