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?
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.
Yes, it applies.
How do I solve it?
Substitute the numbers for the letters.
v = 1/3lwh
What do you mean?
v = volume = 560^3
l = length = 10
w = width = ?
h = height = 14
What then?
Please post what you have now.
560^3 = 1/3 * 10 * 14?
*560^3 =10 * 14?
Yes, the formula you mentioned, V = (1/3)lwh, does apply to this problem. In this formula, V represents the volume of the pyramid, l represents the base length, w represents the base width, and h represents the height of the pyramid.
In this case, you are given that the volume of the pyramid is 560 cubic inches (in^3), the base length is 10 inches, and the height is 14 inches. You are asked to find the base width.
To solve for the base width, we can rearrange the formula and substitute the given values:
V = (1/3)lwh
560 = (1/3)(10)(w)(14)
Now we can solve for w, the base width:
560 = (140/3)w
To isolate the variable, we can multiply both sides of the equation by 3/140:
w = (3/140)(560)
w = 3(4)
w = 12
Therefore, the base width of the square pyramid is 12 inches.