Math 3 Geometry Practice

A farmer had a rectangular enclosure. The width and length ratio of the enclosure is 2:5. The farmer used 500 feet of fencing. What is the area of the enclosure?

• 5,600

• 7623.29

• 12,714.29

• 21,714.29

Answer explanation

Let width = 2x and length = 5x. The perimeter is 2(width + length) = 500.

Tags

CCSS.6.G.A.1

Fred drives an average of 20,000 miles per year and his car goes 20 miles per gallon of gasoline. The average cost of gasoline is $4.25 per gallon. He buys a new car. Fred continues to average 20,000 miles per year, and the average cost of gasoline remains the same. Approximately how many more miles per gallon does the new car get if Fred has a savings of $650 per year on gasoline?

• 3.6 mpg

• 5.8 mpg

• 7.3 mpg

• 10.6 mpg

Answer explanation

Fred drives 20,000 miles at 20 mpg, using 1,000 gallons, costing $4,250. With $650 savings, he spends $3,600, using 847 gallons. New mpg = 20,000/847 ≈ 23.6. Increase = 3.6 mpg.

Tags

CCSS.5.MD.A.1

A box with an open top will be constructed from a rectangular piece of cardboard. The piece of cardboard is 10 inches wide and 12 inches long. The box will be constructed by cutting out equal squares of side x at each corner and then folding up the sides. What is the entire domain for the functions V(x) that gives the volume of the box as a function of x?

• 0<x<5

• x>0

• x>5

• 0<x<12

Tags

CCSS.5.MD.C.5B

CCSS.6.G.A.2

A board is made up of 9 squares. A certain number of pennies is placed in each square, following a geometric sequence. The first square has 2 pennies, the second square has 4 pennies, the third square has 8 pennies. When every square is filled, how many pennies will be used in total?

• 511

• 512

• 1021

• 1022

Answer explanation

The pennies follow a geometric sequence with a common ratio of 2. The total for 9 squares is 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 = 1022. Thus, the correct answer is 1022.

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.2

A shipping company is designing boxes to meet specific requirements. Each box must be a completely closed rectangular prism with no overlapping material. The boxes must hold 36 cans in two layers of 18 cans each. The cans are 3 inches in diameter and 5 inches in height. What is the smallest amount of cardboard needed to meet the specifications?

• 710

• 864

• 963

• 1080

Tags

CCSS.7.G.B.6

David plans to cover the floor of his room with new material. The floor is an isosceles trapezoid whose bases are 10 feet and 16 feet, and sides are 5 feet in length. Each piece of new material has an area of 2.5 square feet. Assuming the pieces of new material can be cut as needed, how many pieces does David need?

• 101

• 37

• 21

• 17

Answer explanation

To find the area of the trapezoid, use the formula: Area = 1/2 * (base1 + base2) * height. The height can be found using the Pythagorean theorem. The area is 52.5 sq ft. Dividing by 2.5 sq ft per piece gives 21 pieces needed.

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GPE.B.7

The vertices of a triangle are (0,0), (8,8), and (12,,4). What is the volume, in cubic units, of the figure created by rotating the triangle about y=x?

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

In parallelogram MNPT, the measure of angle M is (8x+15) degrees and the measure of angle N is (2x+5) degrees. How many degrees is angle P?

• 16

• 37

• 126

• 143

Answer explanation

In parallelogram MNPT, angles M and N are supplementary. Set up the equation: (8x + 15) + (2x + 5) = 180. Solving gives x = 16. Thus, angle M = 143 degrees, and angle P = 143 degrees (equal to angle M).

Tags

CCSS.HSG.CO.C.11

In a rectangle with vertices FGHI and diagonals (FH and GI) intersect at point E. IE=2x+4 and EG=6x-8. What is the length of IG?

• 3

• 6

• 10

• 20

Answer explanation

Set IE = EG: 2x + 4 = 6x - 8. Solving gives x = 3. Substitute x back: IE = 2(3) + 4 = 10, EG = 6(3) - 8 = 10. Since IG = IE + EG, IG = 10 + 10 = 20.

Tags

CCSS.HSG.CO.C.11

County X has a population density of 250 people per square mile. Find the total population of the county if the geometric model of county X is a right triangle with a leg that is 50 miles and a hypotenuse that is 130 miles?

• 75,000

• 415,000

• 750,000

• 812,500

Tags

CCSS.HSG.GMD.A.3