Question

1. numeric 1 point a bucket in the shape of a cylinder is used to carry grain. the bucket has a diameter of 12 inches (in.) and can carry up to 1,584 cubic inches of grain. what is the height of the bucket? use 22/7 for π and round to the nearest hundredth. answer 10. numeric 1 point a bucket in the shape of a cylinder is used to carry grain. the bucket has a diameter of 18 inches (in.) and can carry up to 6,104 cubic inches of grain. what is the height of the bucket? use 22/7 for π and round to the nearest hundredth. answer

Explanation:

Step1: Find the radius of the cylinder

The radius $r$ is half of the diameter. For the first - case, if $d = 12$ inches, then $r=\frac{d}{2}=\frac{12}{2}=6$ inches. For the second - case, if $d = 18$ inches, then $r=\frac{d}{2}=\frac{18}{2}=9$ inches.

Step2: Recall the volume formula for a cylinder

The volume formula of a cylinder is $V=\pi r^{2}h$, where $V$ is the volume, $r$ is the radius, and $h$ is the height. We can solve for $h$: $h=\frac{V}{\pi r^{2}}$.

Step3: Calculate the height for the first case

Given $V = 1584$ cubic inches, $r = 6$ inches, and $\pi=\frac{22}{7}$.
$h=\frac{V}{\pi r^{2}}=\frac{1584}{\frac{22}{7}\times6^{2}}=\frac{1584}{\frac{22}{7}\times36}=\frac{1584\times7}{22\times36}=\frac{11088}{792}=14$ inches.

Step4: Calculate the height for the second case

Given $V = 6104$ cubic inches, $r = 9$ inches, and $\pi=\frac{22}{7}$.
$h=\frac{V}{\pi r^{2}}=\frac{6104}{\frac{22}{7}\times9^{2}}=\frac{6104}{\frac{22}{7}\times81}=\frac{6104\times7}{22\times81}=\frac{42728}{1782}\approx24.09$ inches.

Answer:

For the bucket with diameter 12 inches, the height is 14 inches. For the bucket with diameter 18 inches, the height is approximately 24.09 inches.