Measurement Perimeter, Area, and Volume Changing Dimensions 4/15/2017

Changing Dimensions Perimeter and Area (Rectangles, Triangles, and Circles) When both the dimensions double, the perimeter or circumference doubles, and the area becomes 4 times greater. When both the dimensions triple, the perimeter or circumference triples, and the area becomes 9 times greater. Change (action) Perimeter Area When both dimensions... double x2 x22 = 4 triple x3 x32 = 9 are multiplied by n xn x n2 4/15/2017

Changing Dimensions – Volume (Rectangular Prisms) Changing one dimension: when one dimension doubles, the volume doubles... 21 = 2 when one dimension triples, the volume triples... 31 = 3 Changing two dimensions: when two dimensions double, the volume becomes 4 times greater... 22 = 4. when two dimensions triple, the volume becomes 9 times greater... 32 = 9 Changing three dimensions: when all 3 dimensions double, the volume becomes 8 times greater... 23 = 8 when all 3 dimensions triple, the volume becomes 27 times greater... 33 = 27 4/15/2017

Practice - Changing Dimensions 1. If the length and width of the following rectangle are doubled, what will be the perimeter? 2. If the base and height of the following triangle are tripled, what will be the area? 4/15/2017

Practice - Changing Dimensions 1. If the length and width of the following rectangle are doubled, what will be the perimeter? 2. If the base and height of the following triangle are tripled, what will be the area? ( P= 116 m ) ( A= 810 ft2 ) 4/15/2017

Practice - Changing Dimensions 5. Kasey drew a circle that has a circumference of 13 cm. If he draws another circle with a radius that is 4 times greater, what will be the circumference? 6. A small pizza at Pete’s Pizza has an area of 29 in2. A large pizza has a radius that is triple the radius of a small pizza. What is the area of a large pizza? 3. Gary had a triangular dog pen with a perimeter of 12 ft. He made it bigger by doubling the dimensions. What is the perimeter now? 4. Tara has a rectangular table with an area of 2 m2. She is going to buy another table that has dimensions that are double the first table. What is the area of Tara’s new table? 4/15/2017

Practice - Changing Dimensions 5. Kasey drew a circle that has a circumference of 13 cm. If he draws another circle with a radius that is 4 times greater, what will be the circumference? 6. A small pizza at Pete’s Pizza has an area of 29 in2. A large pizza has a radius that is triple the radius of a small pizza. What is the area of a large pizza? 3. Gary had a triangular dog pen with a perimeter of 12 ft. He made it bigger by doubling the dimensions. What is the perimeter now? 4. Tara has a rectangular table with an area of 2 m2. She is going to buy another table that has dimensions that are double the first table. What is the area of Tara’s new table? ( C = 52 cm.) ( P = 24 ft.) ( A = 8 m2 ) ( A = 261 in2 ) 4/15/2017

Practice - Changing Dimensions 8. Claire’s old aquarium has a volume of 27,000 cm3. She bought a new aquarium in which the length and width are 5 times those of her old tank. What is the volume of Claire’s new aquarium? 9. The swimming pool at the park is shaped like a rectangular prism. The volume of the pool is 800 yd3. The city is going to make the length of the pool twice as long. What will be the volume of the new pool? 7. If the length, width, and height of the rectangular prism are tripled, what will be the volume? 4/15/2017

Practice - Changing Dimensions 8. Claire’s old aquarium has a volume of 27,000 cm3. She bought a new aquarium in which the length and width are 5 times those of her old tank. What is the volume of Claire’s new aquarium? 9. The swimming pool at the park is shaped like a rectangular prism. The volume of the pool is 800 yd3. The city is going to make the length of the pool twice as long. What will be the volume of the new pool? ( V = 675,000 cm3 ) 7. If the length, width, and height of the rectangular prism are tripled, what will be the volume? ( V = 1512 m3 ) ( V = 1600 yd3 ) 4/15/2017

EOG Grade 10 Math – Sample Items-Goal 1 1. If the length of a rectangle is doubled, what will happen to its area? A. the area will be the same B. the area will double. C. the area will triple. D. the area will quadruple. 2. The side measurements of a cube are tripled. What is the ratio of the surface area of the original cube to the larger one? A. 1:3 C. 1:9 B. 1:6 D. 1:12 3. The shadow of a flagpole is 19 ft. long. The shadow of a 12 ft. wall is 4 ft. What is the height of the flagpole? A. 48 ft. C. 62 ft. B. 57 ft. D. 75 ft. 4/15/2017

EOG Grade 10 Math – Sample Items-Goal 1 1. If the length of a rectangle is doubled, what will happen to its area? A. the area will be the same B. the area will double. C. the area will triple. D. the area will quadruple. 2. The side measurements of a cube are tripled. What is the ratio of the surface area of the original cube to the larger one? A. 1:3 C. 1:9 B. 1:6 D. 1:12 3. The shadow of a flagpole is 19 ft. long. The shadow of a 12 ft. wall is 4 ft. What is the height of the flagpole? A. 48 ft. C. 62 ft. B. 57 ft. D. 75 ft. 1. (B) 2. (C) 3. (B) 4/15/2017

EOG Grade 10 Math – Sample Items-Goal 1 The diagram below shows a company’s current packaging of its plant food. 4. The company doubles the radius but keeps the height the same. What effect will this change have on the volume of the container? A. the volume will be 1 ½ times the original B. the volume will be twice the original C. the volume will be three times the original D. the volume will be four times the original 4/15/2017

EOG Grade 10 Math – Sample Items-Goal 1 The diagram below shows a company’s current packaging of its plant food. 4. The company doubles the radius but keeps the height the same. What effect will this change have on the volume of the container? A. the volume will be 1 ½ times the original B. the volume will be twice the original C. the volume will be three times the original D. the volume will be four times the original 4. (D) 4/15/2017