Volume of Cylinders, Cones, Spheres

Volume

Complete the first 3 questions as bell work

Multiple Choice

Find the arc length.

• A

• B

• C

• D

Multiple Choice

Find the arc length.

• A

• B

• C

• D

Multiple Choice

Find the sector area.

• A

• B

• C

• D

Volume

Cylinders, spheres, and cones

Cylinders

The formula for finding the volume of a cylinder is  $V=\pi r^2\times h$  .

In other words....
area of the base (circle) x height

Example:

• First find the area of the base...  $\pi6^2=36\pi$  (diameter is 12 so radius is 6)

• Then multiply the base by the height...  $36\pi\times11=396\pi$  

• Either leave your answer in terms of pi or round to the nearest tenth in the calculator...  $396\pi=396\times\pi=1,244.1$  

Multiple Choice

Find the volume of the cylinder.

• 282.7

• 516.2

• 133

• 214

Multiple Choice

Find the volume of the cylinder. Round to the nearest tenth.

• 124.6 in³

• 88 in³

• 97.5 in³

• 78.9 in³

Multiple Choice

What is the volume of the cylinder? Leave you answer in terms of  $\pi$  

•  $1584\pi\ km^3$  

•  $6336\pi\ km^3$  
  

•  $1584\ km^2$  

•  $4973.76\ km^2$  
  

Cones

A cone holds a third less of the volume of a cylinder. So the volume of a cone is...

  $V=\frac{1}{3}\pi r^2\times h$  

Example:

• Find the area of the base...  $\pi8^2=64\pi$  

• Multiply the base by the height...  $64\pi\times16=1024\pi$  

• Divide that by 3...  $\frac{1024\pi}{3}$  (This fraction doesn't simplify)

• Round if asked.... $\frac{1024\pi}{3}=\frac{3216.99}{3}=1072.33$  

Multiple Choice

Find the volume of the cone. Round your answers to the nearest tenth.

• 113.1 in³

• 37.7 in³

• 339.3 in³

Multiple Choice

Find the volume of the cone. Round your answers to the nearest tenth.

• 320.4 in³

• 314.2 in³

• 942.5 in³

• 267.4 in³

Multiple Choice

What is the volume of the cone? Leave your answer in terms of  $\pi$  

•  $36\pi\ in^2$  
  

•  $54\pi\ in^3$  
  

•  $18\pi\ in^3$  
  

Spheres

The volume of a sphere is based of the radius, just like area and circumference...
 $V=\frac{4}{3}\pi r^3$  

Example:

• Find the radius of the sphere... r=10 because diameter=20

• Plug it into the formula...  $\frac{4}{3}\pi10^3=\frac{4}{3}1000\pi$  

• Simplify...  $\frac{4}{3}1000\pi=\frac{4000\pi}{3}$  

• Round if asked....  $\frac{4000\pi}{3}=\frac{12,566.37}{3}=4,188.8$  

Multiple Choice

Find the volume of the given sphere.

• 1,563.5 cubic in.

• 1,325.5 cubic in.

• 1,129.9 cubic in.

• 1,819.6 cubic in.

Multiple Choice

Find the volume. Round to the nearest tenth.

• 5575.3 cm³

• 506.8 cm³

• 126.65 cm³

• 1393.11 cm³

Multiple Choice

Find the volume of the given sphere. Leave your answer in terms of  $\pi$  

•  $\frac{256\pi}{3}mm^3$  
  

•  $384\pi\ mm^2$  
  

•  $\frac{2048\pi}{3}\ mm^3$  
  

•  $2,144.7\pi\ mm^3$