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04/18/23Page 1
Measurement
• Perimeter, Area, and Volume
• Changing Dimensions
04/18/23Page 2
Changing DimensionsChanging DimensionsPerimeter and Area (Rectangles, Triangles, and
Circles)
When both the dimensions doubledouble, the perimeter or circumference doubles, and the area becomes 4 times greater.
When both the dimensions tripletriple, the perimeter or circumference triples, and the area becomes 9 times greater.
Change (action) Perimeter Area
When both dimensions...
doubledouble x2x2 x2x222 = 4 = 4
tripletriple x3x3 x3x32 2 = 9= 9
are multiplied by n xn x n2
04/18/23Page 3
Changing DimensionsChanging Dimensions – VolumeVolume
(Rectangular Prisms)Rectangular Prisms)
Changing one dimension:Changing one dimension:when one dimension doublesdoubles, the volume doubles... 2211 = = 22when one dimension triplestriples, the volume triples... 3311 = 3 = 3
Changing two dimensions:Changing two dimensions:when two dimensions doubledouble, the volume becomes
4 times greater... 2222 = 4= 4.when two dimensions tripletriple, the volume becomes
9 times greater... 3322 = 9 = 9
Changing three dimensions:Changing three dimensions:when all 3 dimensions doubledouble, the volume becomes
8 times greater... 2233 = 8 = 8when all 3 dimensions tripletriple, the volume becomes
27 times greater... 333 3 = 27= 27
04/18/23Page 4
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?
04/18/23Page 5
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 )( P= 116 m )
( A= 810 ft( A= 810 ft2 2 ))
04/18/23Page 6
Practice - Changing Dimensions3. 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?
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?
04/18/23Page 7
Practice - Changing Dimensions3. 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?
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?
( P = 24 ft.)( P = 24 ft.)
( A = 8 m( A = 8 m22 ) )
( C = 52 cm.)( C = 52 cm.)
( A = 261 in( A = 261 in22 ) )
04/18/23Page 8
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?
04/18/23Page 9
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?
( V = 1512 m( V = 1512 m33 ) )
( V = 675,000 cm( V = 675,000 cm33 ) )
( V = 1600 yd( V = 1600 yd33 ) )
04/18/23Page 10
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 sameB. 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. 1:9B. 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.
04/18/23Page 11
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 sameB. 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. 1:9B. 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)1. (B) 2. (C)2. (C) 3. (B)3. (B)
04/18/23Page 12
EOG Grade 10 Math – Sample Items-Goal 1
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
The diagram below shows a company’s current packaging of its plant food.
04/18/23Page 13
EOG Grade 10 Math – Sample Items-Goal 1
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 original4. (D)4. (D)
The diagram below shows a company’s current packaging of its plant food.
