If the volume of a pyramid with a rectangular base is 500, and has a length of 15 and a height of 4, what is its width?

Question

Sadie Allen · Accepted Answer

#25#

The volume of a pyramid is always one third the area of the base times the height.

Since the base of the pyramid in this problem is a rectangle, its area can be found through #lw#, or #15xxw# since the length is provided.

#V=1/3hlw#

#500=1/3(4)(15)w#

#500=20w#

#w=25#

Claire Akin · Answer

undefined To find the width of the rectangular base of the pyramid, we first need to calculate the area of the base using the given length and height. Then, we can use the formula for the volume of a pyramid to solve for the width.

The area of a rectangle is given by the formula: 
$$ \text{Area} = \text{length} \times \text{width} $$

Given that the length is 15 and the height is 4, we can solve for the width: 
$$ \text{Area} = 15 \times \text{width} = 15\text{width} $$

Now, we can use the formula for the volume of a pyramid, which is given by: 
$$ \text{Volume} = \frac{1}{3} \times \text{base area} \times \text{height} $$

Substitute the known values into the formula: 
$$ 500 = \frac{1}{3} \times (15\text{width}) \times 4 $$

Simplify the equation: 
$$ 500 = \frac{1}{3} \times 60\text{width} $$
$$ 500 = 20\text{width} $$

Now, solve for the width: 
$$ \text{width} = \frac{500}{20} $$
$$ \text{width} = 25 $$

Therefore, the width of the rectangular base of the pyramid is 25.