Volume and Surface Area

3-d shapes beware!

Volume

• Defn: what it takes to fill a 3-d solid

• Units are cubed

• ‘B’ stands for the Area of the shape of the base

• The only solid that doesn’t use ‘B’ is a sphere because it doesn’t have a base.

Examples

• When a vanilla scented candle was new, it was 1 foot tall and the distance across the top of the candle through the wick was 8 inches. How many cubic inches of wax was used to form this candle? Hint: make sure all your units are in inches.

Example 2

• As part of cross-curricular applications, students must tie their research project in Language Arts to all four core subjects. As one part of the relation to math, Nick is going to find out how much paper it took to fill this English-Japanese dictionary in terms of cubic feet. Use the dimensions length: 3ft, width: 18 inches, Height: 42 inches.

Example 3

• There is a large cylindrical aquarium in the center of the new bank. The aquarium’s diameter is 120 inches and its height from the floor to the 12-foot ceiling. What is the approximate capacity of the aquarium in terms of feet. Round your answer to the nearest hundredth.

Surface area:

• Defn: the amount it takes to cover a 3-d solid

• 2 types:– Total: covers everything including the bases– Lateral: covers everything except for the

bases

B: area of the base

P: perimeter of the base

Examples:

• Before a tissue box was opened, the opening in the top was filled with cardboard. Deanna is going to wrap and empty tissue box to use for a ballot box. How much gift-wrapping paper does Deanna need to wrap the entire tissue box?

Example:

• A steam roller is used to pack road surfaces. The front roller has a diameter of 20 inches and the height is 2.5 feet. How much road surface can it come in contact with in one complete rotation in square inches? How about 4 rotations?

Example:

• Holly works in the product analysis division of a sporting business. They are making tents out of a special cloth. The tent includes a material floor. If the tent’s triangle front has a base of 5 feet and a height of 4 feet and the tent is actually 7 ft long, how much material do they need to make the tent? Hint: you need to draw a picture and use the Pythagorean theorem to find a missing measurement.