Question

1. als business sells landscaping supplies and materials. at inventory time, he needs to determine for tax purposes the amount of decorative rock he still has in his piles. the cone - shaped pile of pea gravel has a diameter of 7 m and a height of 4 m.

a. draw a diagram of the pile of pea gravel with dimensions.
b. find the volume of pea gravel in this pile to the nearest cubic metre.

Explanation:

Step1: Calculate the radius

The diameter $d = 7$ m, so the radius $r=\frac{d}{2}=\frac{7}{2}= 3.5$ m.

Step2: Use the volume formula for a cone

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = 3.5$ m and $h = 4$ m into the formula.
$V=\frac{1}{3}\times\pi\times(3.5)^{2}\times4$.
$V=\frac{1}{3}\times\pi\times12.25\times4=\frac{49\pi}{3}\approx\frac{49\times 3.14}{3}\approx51.3$ m³.

Answer:

a. (Since this is text - based response and drawing is not possible here, the description of the diagram would be: Draw a cone. Label the vertical height of the cone as $h = 4$ m and the diameter of the circular base as $d = 7$ m. The radius of the circular base is $r=\frac{7}{2}=3.5$ m.)
b. $51$ m³