b The plant should grow well. See solution for the explanation.
C
c 8.208 pounds
Practice makes perfect
a Let's analyze the given container.
The weight of the container with the soil is 20 pounds and the weight of the container alone is 5 pounds. This tells us that the weight of the soil alone is 15 pounds. We are asked to find the bulk density of the soil. To do this we will find the volume of the soil. Let's use the formula for the volume of a cylinder.
\begin{gathered}
V_\text{soil}=\pi {\color{#0000FF}{r}}^2{\color{#009600}{h}}
\end{gathered}
Since the diameter of the cylinder is 20 inches, its radius is r= 202= 10 inches. The height of the cylinder is h= 25 inches. Let's substitute these values into the formula.
Therefore, the volume of the soil is about 7854 cubic inches. The density of the soil sample is the ratio of its weight to its volume.
Density=Weight/Volume
⇓
Density=15/7854≈ 0.0019
This tells us that the soil's bulk density is about 0.0019 pound per cubic inch.
b The bulk density of the soil from Part A is about 0.0019 pound per cubic inch. This is very close to the desire bulk density of 0.0018 pound per cubic inch. This tells us that the plant should grow well in this soil.
c From Part A we know that the soil's bulk density is about 0.0019 pounds per cubic inch. We are asked to find the weight of the soil if we know that its volume now is 2.5 cubic feet. First, let's convert cubic feet to cubic inches. Since 1 foot=12 inches, we get that 1 ft^3=1728 in^3, because 12^3=1728.
Volume of Soil&=2.5 ft^3=2.5* 1828 in^3
&=4320 in^3
Now, let's use the formula for the density to find the weight of the soil.
