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### Circles:Proportions # High School Geometry: Proportions,Hemispheres

Define linear measurement ( radius and diameter)

Area measure explained

Volume explained

How to convert the linear relationship to an area relationship and a volume relationship

There are several examples of converting from linear to area to volume and keeping the correct ratios

Application problems on surface area and volume A balloon has a radius of 6in. Describe what happens to the balloon’s surface area if the balloon inflates and the radius changes to 12in.

Describe what happens to the same balloon’s volume if the radius is doubled

A sphere has a radius of 4 in. What happens to the sphere’s volume if the radius is halved?

A sphere has a radius of 8in. What happens to the sphere’s surface area if the radius is halved?

Fills in radius,surface area and volume chart   Problems in which you are given area and you need to find volume or given volume and you find area.

A bowling ball has a diameter of 8 inches. Find its volume.

What is the approximate radius of a sphere with a surface area of square 40 pi square feet?

Find the distance traveled in one back-and-forth swing by the weight of a 12-in pendulum that swings through a 75o angle?

A quiche is sliced into 8 equal pieces. The arc length of one piece of quiche is 6.28 inches. What is the diameter of the quiche?

Hemisphere problems

Finding area of a hemisphere

Finding the volume of a hemisphere

Example 1 Given radius find volume