Math Practice Problems for Eighth Grade in Geometry

8G-30) Answer: M’(3,-2), A’(3,-7), T’(-3,-7), H’(-3,-2)

Rectangle MATH has vertices M(1,2), A(1,-3), T(-5,-3), and H(-5,2). What are the coordinates of the rectangle after a translation 2 units right and 4 units down? Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-29) Answer: The new height would need to be ¼ of the original height.

Suppose the radius of a cone is doubled. How could you change the height so that the volume will remain the same? Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-28) Answer: Jeff is correct (Surface area of the Rectangular Prism is 90 sq. m., Surface area of the Cylinder is about 76.9 sq. m)

The two solids have about the same volume. Jeff says that the surface area of the cylinder is less than the surface area of the rectangular solid. Karen disagrees. Who is correct? Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-27) Answer: 4hr. 48 min.

Pipe A can fill an empty tank in 8 hours. Pipe B can fill the tank in 12 hours. If both pipes are used to fill the tank, how long will it take to fill the tank? Give your answer to the nearest minute. Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-26) Answer: 616

A rectangular solid measuring 9” by 12” by 16” is painted blue. The solid is then cut up into 1-inch cubes. How many of the 1-inch cubes have blue on exactly one side? Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-25) Answer: 45

Count the rectangles in the following figure below. Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-24) Answer: 14th

On the following track assume both curves are true half circles. The straight-a-ways of the track are each 2 ¼ miles long. The straight-a-ways are 1 mile apart. During which lap will a race car go over 100 miles? (Use 3.14 for p ) Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-23) Answer: 32

The sides of a square of a garden are increased by 4 m to make a new square garden whose area is 144 sq. m. What was the perimeter of the original garden? Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-22) Answer: 30

In triangle ABC, AD=DE=BE=BC, and mÐABC=140°. What is the degree measure of ÐC? Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-21) Answer: 0

The alternate interior angles formed by the transversal of two parallel lines are complementary. What is the positive difference in the degree measures of these two angles? Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-20) Answer: 210 sq. cm.

The hypotenuse of a right triangle is 37cm and one leg is 12cm. How many square centimeters are in the area of the triangle? Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-19) Answer: 95.03

Jason ties the leash of his dog Skip to the corner of a doghouse. The dimensions of the doghouse are 3 ft. by 4 ft., and the leash is 6ft. long. Over how many square feet can John’s dog wander? Express your answer as a decimal to the nearest hundredth. Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-18) Answer: 4

If the length of each side of a rectangular pool must be a multiple of 3 ft., how many different perimeters are possible that yield an area of 360ft² ? Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-17) Answer: East
You are facing east. You turn left, then left again, then turn about-face. Which direction are you finally facing? Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-16) Answer:  two
If an eight-inch square cake serves four people, how many twelve-inch square cakes are needed to provide equivalent servings to eighteen people?  Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-15) Answer:  circle
Three shapes - a circle, a rectangle, and a square - have the same area.  Which shape has the smallest perimeter? Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-14) Answer:   8,000
What is the maximum number of cubes measuring 5 cm on an edge that can be obtained by cutting a solid cube that measures 1 m on an edge?  Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-13) Answer:     8
If exactly five diagonals can be drawn from one vertex of a convex polygon, how many sides does the polygon have? Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-12) Answer:    20
The width of a rectangle is increased by 6 inches while the length is decreased by 2 inches. The resulting rectangle is a square with perimeter 28 inches. What was the number of inches in the perimeter of the original rectangle? Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-11) Answer:    567
An octagon is inscribed in a square so that the vertices of the octagon trisect the sides of the square. The perimeter of the square is 108 centimeters. What is the number of square centimeters in the area of the octagon? Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-10) Answer:     56
How many distinct triangles can be formed by connecting three different vertices of a cube?  Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-9) Answer:    24Ö3
A new solid is formed by gluing a face of one regular tetrahedron to a face of an identical tetrahedron. The length of one edge of a tetrahedron is 4 inches. How many square inches are in the surface area of the new solid? Express your answer in simplest radical form.  Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-8) Answer:    20
A rectangular floor measuring 10 feet by 12 feet is tiled with one-foot square tiles. Through how many tiles would the diagonal of this rectangle pass?  Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-7) Answer:    32pi
A square is inscribed in a circle. The area of the square is 64 square inches. How many square inches are in the area of the circle? Express your answer in terms of pi. Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-6) Answer:    55
Each dimension of a parallelogram is increased to four times its original size to form a similar parallelogram. If the new parallelogram has an area of 880 square units, what is the number of square units in the area of the original parallelogram? Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-5) Answer:    8 & part of 9th
The university recently purchased an enormous electric polisher for cleaning their radio satellite dish. The company selling the polisher has guaranteed clearer messages and less static or the entire purchase price is refunded. The polisher is on a long pole which is attached to the center of the dish. The mop-like polishing device has a 4-foot-wide-cleaning head that reaches to the outside edge of the dish. The polisher goes around in circles, moving toward the middle of the dish. If the dish is 234 feet across, how many trips around are needed to clean 1/2 of the area of the dish? Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-4) Answer:    82" cable
Deep inside an iceberg archaeologists have discovered the lost continent of Alopecia. The Alopecians were hairless creatures who left behind a magnificent temple of ice with 1-foot thick floors and walls. Buried beneath the floor of the third and bottom level is the statue of the goddess Henna, sculpted of ice and set with diamonds. A diving team will try to remove the statue. However, the only access is by drilling through the 1-foot thick layers of ice that divide the levels, so the statue will have to be pulled out by cable. Each level is 16 chambers wide by 32 long, running west to east. The 512 identical chambers on each level are 3 feet square by 3 feet high. Because each chamber has four walls, a ceiling, and floor; divers will drill holes in the middle of a chamber roof, pull the cable along the center of each chamber right under the ceiling, and drill through the wall into the next chamber. They will follow this plan: Drill hole through the center of the roof above the most southeastern chamber; go 2 chambers west, 4 chambers north; drop to next level; go 4 chambers northwest, 8 chambers west; drop to bottom level. The statue is buried 3 feet deep beneath the floor of this chamber. What is the shortest length of cable the divers will need to remove the statue? Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-3) Answer:    18" ring
Lin Po is watching his friend Chun make a dart board Chun has drawn a series of concentric circles around a central circle. The diameter of the outer circle is 30 inches, the diameter of the next smaller circle is 24 inches, the diameter of the next smaller circle is 18 inches, and so on. "Hey, Chun:' challenges Lin Po. "Can you figure out the area of each of the rings?" "Sure," Chun answers smartly. "I'll use 3.14 for pi." "Good," challenges Lin Po again. "Can you figure out which ring has an area equal to one-fifth the area of the whole board?" Chun has to think about that. Can you help him?  Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-2) Answer:    about 16.97 inches
A municipality is replacing its water supply lines. The current system uses two identical pipes that have circular cross-sections, each with a diameter of one foot. The town decides to use a single replacement pipe with the same capacity. What is the diameter of the new pipe? Explain in detail how you found your answer using words, numbers, and/or pictures.

8G-1) Answer:    56 feet
Jones High School is constructing a circular ice-skating rink. It wants to design the rink so that 15 trips around the outside rail will equal 1 mile. To the nearest foot, what should be the radius of the rink? Explain in detail how you found your answer using words, numbers, and/or pictures.

Share a problem (thank you) to add to this list and submit to:   donna_buck@pasd.wednet.edu Please title the subject "Problems for 8G" and include the answer.