Question

a company that manufactures storage bins for grains made a drawing of a silo. the silo has a conical base, as shown below. which of the following could be used to calculate the total volume of grains that can be stored in the silo? π(10ft)²(2ft) + 1/3π(2ft)²(13ft - 10ft), π(2ft)²(10ft) + 1/3π(2ft)²(13ft - 10ft), π(10ft)²(2ft) + 1/3π(13ft - 10ft)²(2ft), π(2ft)²(10ft) + 1/3π(13ft - 10ft)²(2ft)

Explanation:

Step1: Identify the shapes and volume formulas

The silo consists of a cylinder and a cone. The volume of a cylinder is $V_{cylinder}=\pi r^{2}h$ and the volume of a cone is $V_{cone}=\frac{1}{3}\pi r^{2}h$. The radius $r = \frac{4}{2}=2$ ft. The height of the cylinder $h_{cylinder}=10$ ft and the height of the cone $h_{cone}=13 - 10=3$ ft.

Step2: Calculate the volume of the cylinder

Using the formula $V_{cylinder}=\pi r^{2}h$, with $r = 2$ ft and $h = 10$ ft, we get $V_{cylinder}=\pi(2\text{ft})^{2}(10\text{ft})$.

Step3: Calculate the volume of the cone

Using the formula $V_{cone}=\frac{1}{3}\pi r^{2}h$, with $r = 2$ ft and $h=13 - 10 = 3$ ft, we get $V_{cone}=\frac{1}{3}\pi(2\text{ft})^{2}(13\text{ft}- 10\text{ft})$.

Step4: Calculate the total volume

The total volume $V = V_{cylinder}+V_{cone}=\pi(2\text{ft})^{2}(10\text{ft})+\frac{1}{3}\pi(2\text{ft})^{2}(13\text{ft}- 10\text{ft})$.

Answer:

$\pi(2\text{ft})^{2}(10\text{ft})+\frac{1}{3}\pi(2\text{ft})^{2}(13\text{ft}- 10\text{ft})$