Math 6/7 NOTES (10.2) Notes Name: Volume and Surface Area of Rectangular Prisms & Cylinders VOLUME o Volume is the measure of occupied by a solid region. When measuring volume, the units will be cubed. A cubic centimeter (cm 3 ) is a cube whose edges all measure 1 centimeter. VOLUME of Rectangular Prisms o The formula for the volume of a rectangular prism is: Find the volume of each rectangular prism. Round to the nearest tenth if necessary. 1. 2. VOLUME of Cylinders o The formula for the volume of a cylinder is: Find the volume of each cylinder. Use 3.14 as π. Round to the nearest tenth if necessary. 1. 2.
SURFACE AREA Surface Area is the of the areas of all faces of a solid object. 1 cm When measuring surface area, the units will be squared. 1 cm A square centimeter (cm 2 ) is a square whose sides all measure 1 centimeter. SURFACE AREA of Rectangular Prisms o Rectangular Prisms have 6, four-sided faces. o Formula for the volume of a rectangular prism: SA = Find the surface area of each rectangular prism. Round to the nearest tenth if necessary. 1. 2. 3.
SURFACE AREA of Cylinders o Cylinders are made up of one rectangle and two congruent circles. o The length of the rectangle is equal to the circumference of one circle. o The formula for the surface area of a cylinder is: Find the surface area of each cylinder. Use 3.14 as π. Round to the nearest tenth if necessary. 4. 5. 6.
How does the VOLUME of a rectangular prism change when one of the attributes is increased? Scale Factor l w h V Original Prism 4 3 2 Length 2 3 2 Width 2 Height 2 Conclusion: When the length of one of the attributes of the prism is changed by a scale factor, the volume For example, doubling the length of a prism will its volume. Example: A company is producing three sizes of cereal. The family-size is 2.5 times wider than the original box, while the smallest has 1 of the height of the 2 original box. Compare the amounts of cereal the boxes can hold. Scale Factor l w h V Original Box 7.5 in 2.5 in 12 in Family Size Smallest Size How does the SA of a rectangular prism change when one of the attributes is changed? Scale Factor l w h SA Original Prism 3 2 4 Length 2 Width 2 Height 2 Length 3 Compare the surface area of your original prism to the surface area of new prisms, and explain how changing an attribute affects surface area.
Math 6/7 Homework (10.2) Volume and Surface Area of Rectangular Prisms & Cylinders 1. The inside of a refrigerator in a medical laboratory measures 17 in by 18 in by 42 in. How many cubic inches can it hold? 2. A birthday gift is placed inside the box shown. What is the minimum amount of wrapping paper needed to wrap this gift? 14 in. 10 in. 7 in. 3. How much metal was used to make this can of soup? 3 cm 4. Refer to problem #3. When full, how much soup does the can contain? 5 cm 5. Lawrence is donating some outgrown clothes to charity. How many cubic feet of clothes will fit in the box? 6. All sides of this wafer are to be covered in frosting. Calculate how much should be covered. 4 ft. 3 ft. 2 ft. 1 2 in. 2 in. 1 in.
7. Monique and Kiana want to give their friend a birthday present. They have put the present into a shoebox and now they want to wrap the box. a. How much wrapping paper will they need. If the shoebox is 1 foot long, 8 inches wide and 6 inches high? (hint: must have the same units) 8. Ian bought a can of soup to give to his friend. Now he would like to wrap the can with paper. a. If the can has a circular base with a diameter of 4 inches, a height of 6 inches, how much wrapping paper will Ian need? b.how much paper if the shoebox is twice as long? b.how much paper if the can is twice as tall? c. How much air does the empty shoebox hold? c. How much soup will the can hold? d. How much air if the shoebox is twice as long? d. How much soup if the can is twice as tall? 9. A standard 20-gallon aquarium tank is a rectangular prism with length 24 in, width 12 in, and the height 20 in. Which side could you double, to increase the volume the most? 10. Plastic was used to make a rectangular prismshaped container of baby food that is 2 in high, 1 in long, and 1.5 in wide. If you doubled each of the 3 sides, one at a time, which of the three new containers would use the least plastic?