Question

find the volume specified. use 3.14 as the approximate value of pi, and round your answer to the nearest tenth.find the volume of a feed bin having the shape of a right circular cylinder of radius 5 ft and height 5 ft topped by a right circular cone of the same radius and height 3 ft Draw a picture to get started.

Answer 1

The volume of the bin is 471 cubic feet

EXPLANATION;

Given that;

The radius of the cylinder is 5ft

The height of the cylinderis 5 ft]

The height of the cone s 3ft]

To find the total volume of the bin, follow the steps below

Firstly, draw the structure of the bin

Secondly, Write the formula for calculating the volume of a cone and a cylinder

`\begin{gathered} \text{ The volume of a cone = }(1)/(3)\pi r^2h \\ \text{ The volume of a cylinder = }\pi r^2h \end{gathered}`
`\begin{gathered} \text{ The volume of the cone = }(1)/(3)\pi r^2h \\ \text{ where }\pi\text{ = 3.14} \\ \text{ The volume of the cone = }(1)/(3)*\text{ 3.14 }*\text{ 5}^2\text{ }*\text{ 3} \\ \text{ The volume of the cone = }(1)/(3)*\text{ 3.14 }*\text{ 25 }*\text{ 3} \\ \text{ The volume of the cone }=3.14\text{ }*\text{ 25} \\ \text{ The volume of the cone = 78.5 ft}^3 \end{gathered}`
`\begin{gathered} \text{ The volume of the cylinder = }\pi r^2h \\ \text{ }\pi\text{ = 3.14} \\ \text{ The volume of the cylinder = 3.14 }*\text{ 5}^2\text{ }*\text{ 5} \\ \text{ The volume of the cylinder = 3.14 }*\text{ 25 }*\text{ 5} \\ \text{ The volume of the cylinder = 392.5 ft}^3 \end{gathered}`

Find the volume of the bin

`\begin{gathered} \text{ Volume of the bin = volume of the cone + volume of cylinder} \\ \text{ Volume of the bin = 78.5 + 392.5} \\ \text{ Volume of the bin = 471 ft}^3 \end{gathered}`

Hence, the volume of the bin is 471 cubic feet