1). A square pyramid has a volume of 560 in to the third power, a base length of 10 in., and a height of 14 in. What is its base width?
2). h + p = 3(k-8)
My textbook states that the formula v = 1/3lwh relates the volume of a square pyramid to its base length l, width w, and height h. However, I am uncertain whether this information applies to this equation or not.
1.
of course it does
I noticed Ms Sue helped you with this already.
http://www.jiskha.com/display.cgi?id=1381185368
Why did you not follow her suggestion??
But more important:
You are told the base is a square,
if the length is 10
wouldn't the width be 10 also ??
checking:
(1/3)(10)(10)(14) = (1/3)(1400) ≠ 560^3
So your question has false data and is bogus.
2. what do you want done with this equation?
2). I suppose I am supposed to solve it.
1) To find the base width of a square pyramid, we need to use the formula for the volume of a pyramid, which is given by:
Volume = (1/3) * base area * height
In this case, we are given the volume (560 in^3), the base length (10 in), and the height (14 in). Let's substitute these values into the formula and solve for the base area:
560 = (1/3) * base area * 14
560 = (14/3) * base area
Now, let's isolate the base area by multiplying both sides of the equation by 3/14:
560 * (3/14) = base area
120 = base area
The base area of the square pyramid is 120 square inches.
To find the base width, we need to determine the length of one side of the square base. Since it is a square, all sides have the same length. Let's call this length "x".
Now we can use the formula for the area of a square, which is given by:
Area = side length * side length
In our case, the area is 120 square inches and the side length is x:
120 = x * x
120 = x^2
To find x, we can take the square root of both sides of the equation:
sqrt(120) = sqrt(x^2)
sqrt(120) = x
Therefore, the base width of the square pyramid is approximately 10.95 inches.
2) The equation h + p = 3(k-8) represents a linear equation with three variables: h, p, and k. To solve for one variable in terms of the others, we need a bit more information or additional equations.
If you want to isolate one variable, we can rearrange the equation to solve for h:
h = 3(k-8) - p
Alternatively, we can rearrange the equation to solve for p:
p = 3(k-8) - h
If you have specific values for any two of the variables (h, p, or k), you can substitute them into the equation to find the value of the third variable.