8th Grade EOG Review

Sandra Davidson, MaEdNBCT EA Math

Lakeshore Middle School

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Measurement

• Perimeter, Area, and Volume

• Changing Dimensions

• Indirect Measurement

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Measurement of a Triangle

The sum of the measures of the interior angle equals 180°.

Write an equation and solve for x:

32 + 100 + x = 180 132 + x = 180 -132 -132

xx = 48° = 48°

What is the value of x in the following triangle?

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Perimeter and Circumference

PerimeterPerimeter is the distance around the outside of a plane figure.

This distance is called the circumferencecircumference when the figure is a circle.

P = S1 + S2 + S3 + S4 + S5 C = π d

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Area – the measure of square units inside a plane figure.

A = ½ A = ½ bhbh A = A = bhbh

A = A = bhbh A = A = ππ rr22

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Practice – Area, Perimeter and Circumference1. Paul want to build a

rectangular dog pen. He has 24 ft. of fencing in 1-ft. sections. What are the dimensions of the best dog pen he can build?

2. Paul decides to use a wall of the house as one side of the rectangular dog pen. If he uses the 24 ft. of fencing for the other 3 sides, what are the dimensions of the best dog pen he can build?

3. Carlos bought a pizza that had an area of 201 in2. He paid $8.99 for the pizza. Tameka bought two pizzas, each of which had an area of 133 in2. She paid a total of $10.99 for the two pizzas.What is the approximate diameter of each pizza?

Which pizza is the better buy based on the number of square inches per pizza?

( 6 ft. x 6 ft.)( 6 ft. x 6 ft.)

( 8 ft. X 8 ft.)( 8 ft. X 8 ft.)

( d = 16 in. and 13 in.)( d = 16 in. and 13 in.)

(Tameka, $0.04/sq. in. - while (Tameka, $0.04/sq. in. - while Carlos, $0.05/sq. in.)Carlos, $0.05/sq. in.)

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Practice – Area, Perimeter and Circumference1. Paul want to build a

rectangular dog pen. He has 24 ft. of fencing in 1-ft. sections. What are the dimensions of the best dog pen he can build?

2. Paul decides to use a wall of the house as one side of the rectangular dog pen. If he uses the 24 ft. of fencing for the other 3 sides, what are the dimensions of the best dog pen he can build?

3. Carlos bought a pizza that had an area of 201 in2. He paid $8.99 for the pizza. Tameka bought two pizzas, each of which had an area of 133 in2. She paid a total of $10.99 for the two pizzas.What is the approximate diameter of each pizza?

Which pizza is the better buy based on the number of square inches per pizza?

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Volume - the measure of cubic units inside a

3-D figure.

What is the volume of this rectangular prism?

V = BBhV = l x wl x w x hV = 2.5 x 1.5 x

1.6V = 6 m6 m22

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Surface Area – the measure of square units of the outside “wrapping” of a 3-D

figure.

What is the surface area?Find the area of the frontfront:

2.5 x 1.6 = 44and area of the right side:

1.5 x 1.6 = 2.42.4and the area of the toptop:

2.5 x 1.5 = 3.753.75Add these and multiply by 2multiply by 2:

22(44 + 2.42.4 + 3.753.75) = 20.320.3 mm22

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Practice - Volume and Surface Area

What is the volumevolume of this rectangular prism?V = BBhV = l x wl x w x hV = 8 x 8 x 7V = 448 m448 m33

What is the surface areasurface area?front: 8 x 7 = 5656side: 8 x 7 = 5656top: 8 x 8 = 6464

22(5656 + 5656 + 6464) = 352 m352 m22

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Practice - Volume and Surface Area

What is the volumevolume of this cylinder?V = BBhV = ππ r r22 x hV = 3.14 x22 x 16V = 200.96 inV = 200.96 in33 (or 64π)

What is the surface areasurface area?top: 3.14 x 222 = 12.5612.56bottom: 3.14 x 222 = 12.5612.56label: CC x 16 (circumference x 16)

ππdd x 16 3.14 x 4 x 16 = 200.96200.96 in2

12.56 + 12.56 + 200.96 = 226.08 in2

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Practice - Volume and Surface AreaWhat is the volume of this

triangular prism?V = BBhV = ½ ½ ((bb x x hh)) x hV = ½ (6 x 4) x 8V = 96 ft96 ft33

What is the surface area?top/bottom: ½ (6 x 4) = 1212 3 rect. sides: 3(6 x 8) = 144144

1212 + 1212 + 144144 = 168 168 ftft22

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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

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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

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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?

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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 ))

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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?

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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 ) )

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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?

Practice: Buckle Down ( pp. 160 – 162 )Practice: Buckle Down ( pp. 160 – 162 )

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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 ) )Practice: Buckle Down ( pp. 160 – 162 )Practice: Buckle Down ( pp. 160 – 162 )

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Indirect Measurement

Apply the concepts of similar figures to find the unknown measurement of an object that is nearly impossible to measure with a common measuring tool.

What is the distance across the lake?

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Indirect Measurement

Apply the concepts of similar figures to find the unknown measurement of an object that is nearly impossible to measure with a common measuring tool.

What is the distance across the lake? ( 48 ft.)( 48 ft.)

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EOG Grade 8 Math – Sample Items-Goal 1(released by NC DPI)

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.

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EOG Grade 8 Math – Sample Items-Goal 1(released by NC DPI)

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)

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EOG Grade 8 Math – Sample Items-Goal 1(released by NC DPI)

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.

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EOG Grade 8 Math – Sample Items-Goal 1(released by NC DPI)

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.

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EOG Grade 8 Math – Sample Items-Goal 1(released by NC DPI)

5. Jake wanted to measure the length of the pond, so he drew this diagram of two similar triangles.

What is the approximate length of the pond?A. 25 ft.B. 19 ft.C. 18 ft.D. 13 ft.

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EOG Grade 8 Math – Sample Items-Goal 1(released by NC DPI)

5. Jake wanted to measure the length of the pond, so he drew this diagram of two similar triangles.

What is the approximate length of the pond?A. 25 ft.B. 19 ft.C. 18 ft.D. 13 ft.

4. (D)4. (D)