Lesson

 

Notes

 

Questions

\(\textbf{1)}\) Find the volume and surface area of the below cylinder.

Show Volume

The volume is \( 160\pi\approx502.65\) m\(^3 \)

Show Surface Area

The surface area is \( 112\pi\approx351.86\) m\(^2 \)

 

\(\textbf{2)}\) A cylinder has volume \( 32\pi \) ft\(^3\) and height \(8\) ft. What is the radius?

Show Radius

The radius is \( 2 \) ft

Show Work

\(\,\,\,\,\,\,\text{Volume of Cylinder}=\pi r^2 h\)
\(\,\,\,\,\,\,(32\pi)=\pi r^2 (8)\)
\(\,\,\,\,\,\,4=r^2\)
\(\,\,\,\,\,\,2=r\)

 

See Related Pages\(\)

\(\bullet\text{ Geometry Homepage}\)
\(\,\,\,\,\,\,\,\,\text{All the Best Topics…}\)

\(\bullet\text{ Rectangular Prisms- Volume}\)
\(\,\,\,\,\,\,\,\,\)\(V=l \cdot w \cdot h…\)

\(\bullet\text{ Rectangular Prisms- Surface Area}\)
\(\,\,\,\,\,\,\,\,\)\(SA=lw+wh+lh…\)

\(\bullet\text{ Distance Formula 3D}\)
\(\,\,\,\,\,\,\,\,d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2…}\)

\(\bullet\text{ Diagonal of a Prism}\)
\(\,\,\,\,\,\,\,\,\)\(d=\sqrt{l^2+w^2+h^2}…\)

\(\bullet\text{ Pyramids- Volume and Surface Area}\)
\(\,\,\,\,\,\,\,\,\)\(V=\frac{1}{3}Bh\,\,\,SA=B+\frac{pl}{2}…\)

\(\bullet\text{ Cones- Volume and Surface Area}\)
\(\,\,\,\,\,\,\,\,\)\(V=\frac{1}{3}\pi r^2 h\,\,\,SA=\pi r^2+\pi r l…\)

\(\bullet\text{ Spheres- Volume and Surface Area}\)
\(\,\,\,\,\,\,\,\,\)\(V=\frac{4}{3}\pi r^3 \,\,\,SA=4 \pi r^2…\)

\(\bullet\text{ Similar figures}\)
\(\,\,\,\,\,\,\,\,\text{Similarity ratio } a:b, \text{Area ratio } a^2:b^2, \text{Volume ratio } a^3:b^3\)

\(\bullet\text{ Nets of Polyhedra}\)
\(\,\,\,\,\,\,\,\,\)

 

In Summary

The volume of a cylinder is a measure of the amount of space contained within the cylinder. It is calculated by multiplying the base area of the cylinder by its height. The surface area of a cylinder is a measure of the total area of the lateral surface and the two circular ends of the cylinder. It is calculated by adding the area of the two circular ends to the lateral surface area of the cylinder. Volume and surface area of cylinders are typically covered in a high school geometry class. We learn about volume and surface area of cylinders because they are important concepts in geometry and are commonly used in real-world applications, such as in engineering and construction.