Question

a conical pile of sand has a base radius of 267 cm and a vertical height of 134 cm. the volume of sand in the pile is closest to?

Explanation:

Step1: Recall the formula for the volume of a cone

The volume \( V \) of a cone is given by the formula \( V=\frac{1}{3}\pi r^{2}h \), where \( r \) is the radius of the base and \( h \) is the height of the cone.

Step2: Substitute the given values into the formula

We are given that \( r = 267\space\text{cm} \) and \( h=134\space\text{cm} \). Substituting these values into the formula, we get:
\( V=\frac{1}{3}\times\pi\times(267)^{2}\times134 \)
First, calculate \( (267)^{2}=267\times267 = 71289 \)
Then, multiply by \( 134 \): \( 71289\times134=71289\times(100 + 30+4)=7128900+2138670 + 285156=7128900+2138670=9267570+285156 = 9552726 \)
Now, multiply by \( \frac{1}{3}\pi \): \( V=\frac{1}{3}\times\pi\times9552726=3184242\pi \)
Using \( \pi\approx3.1416 \), we have \( V\approx3184242\times3.1416 \)
\( 3184242\times3.1416 = 3184242\times(3 + 0.1416)=3184242\times3+3184242\times0.1416=9552726+451088.6672 = 9993814.6672\space\text{cubic centimeters} \)

Answer:

The volume of the sand pile is closest to \( 10000000\space\text{cm}^3 \) (or more precisely approximately \( 9993815\space\text{cm}^3 \))