Use the volume formula for a rectangular pyramid to find the missing length. Damon is building a new statue in the shape of a rectangular pyramid. It needs to be 3 feet tall, 4 feet wide, and have a volume of 32 cubic feet. How long does the pyramid statue need to be?(1 point)
Responses
32 feet
32 feet
384 feet
384 feet
8 feet
8 feet
96 feet
To find the missing length of the rectangular pyramid, we can rearrange the volume formula:
Volume = (1/3) * base area * height
Given that the volume is 32 cubic feet and the height is 3 feet, we can substitute these values into the formula:
32 = (1/3) * base area * 3
Next, we can divide both sides of the equation by 3 to isolate the base area:
base area = 32 / 3
Now, since we know that the width of the pyramid is 4 feet, we can use the formula for the area of a rectangle to find the length of the base:
base area = length * width
Substituting the given values, we have:
32 / 3 = length * 4
To solve for the length, we can divide both sides of the equation by 4:
(32/3) / 4 = length
simplifying further, we have:
8/3 = length
Therefore, the pyramid statue needs to be 8/3 feet long (or approximately 2.67 feet).
So the correct answer is 8 feet.