Name: _______________________________________ Volume, Area, and Perimeter using Cube and Square Roots 1. If you are working with the label inches, what would be the label for the following? Area: ______________ Surface area: _______________ Perimeter: ____________ Side length: ____________ Volume: _______________ 2. A cube has a side length of 6 cm. Using exponents, show how you would find the volume. How would you find the area of one face? Area of one face (using exponents):_________ Volume (using exponents): _______ Now solve: Area: _________________ Volume: ____________________ 3. Area of a square=16 square inches. Draw the square and label the side lengths. 4. The volume of a cube is 512 in3. Draw the cube and label the side lengths. 5. If a cube has a side length of 4.5 inches, find the volume and the area of all 6 sides together. Volume: Area of all 6 sides: 6. The area of a square is 81 square cm. Draw the square and label the side lengths. Then find the perimeter. 7. Would you classify 100 as a perfect square, a perfect cube, both, or none? Why? 8. Would you classify 1 as a perfect square, a perfect cube, both, or none? Why? 9. The construction company in charge of the new playground wants to put a barrier around the playground to keep all the wood shavings inside. The playground is 625 square feet. How many feet of barrier do they need? 10. Karen wants to build a fence around her yard. She knows that her yard is a perfect square and has an area of 36 ft2. How much fence does she need for her yard? 11. The Jones Building Company makes tiny homes in a perfect cube. They love to show their customers how much space there is by giving not only the square feet but also the cubic feet. They are advertising their latest tiny home having 1728 cubic feet and 121 square feet. They are getting lots of phone calls about their math. Why? 12. Santa Claus is having his elves wrap all the presents in boxes shaped as cubes that are the exact same size to help with hauling the presents in his sleigh. Each box is 216 cubic feet. How wide is each box? 13. Using the information from number 12, if Santa’s sleigh is 72 feet long, how many rows of boxes can he fit?