Question

1 a shipping container in the form of a cylinder has a radius of 6 feet and a length of 54 feet. what is the volume of the container, in cubic feet, rounded to the nearest tenth? 6104.8 cubic feet 2 a sphere has a radius of 4 feet. what is the volume, in cubic feet, of the sphere rounded to the nearest hundredth? 267.95 cubic feet 3 ellie orders a single scoop of vanilla ice cream. she notices that the ice cream is packed inside the cone and forms half of a sphere above the cone. the height of the cone is 5 inches and the radius of both the cone and the half - sphere is 1 inches. select the answer in terms of pi that is the total volume, in cubic inches, of ice cream inside and above the cone. a ( 1pi ) b ( 3.5pi ) c ( \frac{7}{3}pi ) d ( \frac{2}{3}pi ) 4 a cone has a height of 11 meters and a radius of 4 meters. what is the volume of the cone, in cubic meters, rounded to the nearest hundredth? 586.43 cubic meters

Explanation:

Step1: Calculate the volume of the cone

The formula for the volume of a cone is $V_{cone}=\frac{1}{3}\pi r^{2}h$. Given $r = 1$ inch and $h = 5$ inches, we substitute these values into the formula:
$V_{cone}=\frac{1}{3}\pi\times(1)^{2}\times5=\frac{5}{3}\pi$

Step2: Calculate the volume of the hemisphere

The formula for the volume of a sphere is $V_{sphere}=\frac{4}{3}\pi r^{3}$. For a hemisphere, the volume is $V_{hemisphere}=\frac{2}{3}\pi r^{3}$. Given $r = 1$ inch, we substitute:
$V_{hemisphere}=\frac{2}{3}\pi\times(1)^{3}=\frac{2}{3}\pi$

Step3: Calculate the total volume of the ice - cream

The total volume $V = V_{cone}+V_{hemisphere}$.
$V=\frac{5}{3}\pi+\frac{2}{3}\pi=\frac{5 + 2}{3}\pi=\frac{7}{3}\pi$

Answer:

C. $\frac{7}{3}\pi$