College Math Prep A - Unit 2

Sydney fills half the volume of a container with decorative sand. The container is cylindrical with a hemisphere attached to one end. The cylinder and hemisphere each have a diameter of 10 inches, and the cylinder has a length of 25 inches. The sand costs 4 cents per cubic inch. What is the approximate cost of the sand in the container?

$45

Natalie put seed in a patch of her backyard for a new lawn. The area seeded is 450 ft.^2 and the seed costs $0.15 per square foot. How much did Natalie pay for the seed?

$67.50

Martin designed a glass bead that was a right cylinder with a cylindrical hole through the center of the bases. The outer cylinder had a diameter of 1 centimeter, the inner cylinder had a diameter of 0.5 centimeters, and the height of the bead was 1.5 centimeters. Approximately how many cubic centimeters of glass were in the bead?

0.88 cubic centimeters

A prescription medication company produces a capsule shaped like a cylinder with a hemisphere attached to each base. The cylinder and hemispheres all have a diameter of 8 millimeters, and the cylinder has a height of 15 millimeters. What is the approximate volume of the capsule?

1,022 mm^3

A square pyramid has a base edge length of 14 feet and a slant height of 25 feet. What is the volume of the pyramid, rounded to the nearest whole number if necessary?

1,568 ft.^3

Jason made a spherical cake pop that is 1..3 inches in diameter. What is the approximate volume of the cake pop?

1.15 in.^3

Mason purchased a rectangular poster that was 2.5 feet wide and 3.5 feet tall. He used decorative tape to make a frame around the edge of the poster. What is the length of the tape that he used around the edge of the poster?

12 feet

A cylinder has a radius of 15 millimeters and a height of 17 millimeters. What is the approximate volume of the cylinder?

12,017 cubic millimeters

A canning company uses sheet metal to make its cans. One can that it makes has a diameter of 5 inches and a height of 5.5 inches. Approximately how much sheet metal is needed to make this can?

126 square inches

Marcus painted one wall of his entryway as an accent wall. The wall is a trapezoid, where the shorter side is 9 feet tall and the longer side is 15 feet tall. The length of the wall is 13 feet. He did not paint the door, which is 7 feet by 2.5 feet. He also did not paint the triangular window, which has a height of 3 feet and a base of 6 feet. What is the area of the wall that Marcus painted?

129.5 square meters

Andie created a clay model of a building for a display by attaching a right square pyramid to a cube. The pyramid had a base edge length of 6 inches and a slant height of 5 inches. The cube had an edge length of 4.5 inches. Approximately how many cubic inches of clay did Andie need to create the building?

139 cubic inches

Stacy made a square tablecloth with a side length of 3.5 feet. She put lace along each side of the tablecloth. How much lace did Stacy need for the tablecloth?

14 feet

A canning company uses sheet metal to make its cans. One can that it makes has a diameter of3.5 inches and a height of 1.5 inches. What is the approximate volume of this can?

14.4 in.^3

Andie created a model of a building for a display by attaching a right square pyramid to a cube and then attaching it to a display board. The pyramid had a base edge length of 6 inches and a slant height of 5 inches. The cube had an edge length of 4.5 inches. She painted the visible surfaces of the figure after she attached it to the board. What was the area of the model that Andie painted?

156.75 in.^2

Jun made a round tablecloth for his kitchen table. The tablecloth is 4.5 feet in diameter. Approximately how much fabric did Jun use for the tablecloth?

16 ft.^2

Tran painted pieces for a model she is building. She painted one cone-shaped piece with a diameter of 3 inches and a slant height of 2 inches using silver paint. What is the approximate area Tran painted silver?

16.5 in.^2

Jasmine put new tile on her bedroom floor. Her bedroom measures 12 feet by 14 feet. How much tile did Jasmine need to cover the entire floor?

168 square feet

A snack bar sells popcorn in a cone-shaped container. The container has a height of 8 inches and a diameter of 9 inches. What is the approximate volume of the popcorn container?

170 cubic inches

What is the approximate perimeter of a semicircle with a diameter of 7 inches?

18 inches

Martin designed a bead that was a right cylinder with a cylindrical hole through the center of the bases. The outer cylinder had a radius of 1 centimeter, the inner cylinder had a radius of 0.5 centimeters, and the height of the bead was 1.5 centimeters. After creating the bead, he covered the entire bead with a protective coating. What was the approximate area of the bead that Martin covered?

18.85 cm^2

Jamie sanded the top surface of an old desk so she could refinish it. The desktop measured 65 inches by 35 inches and had two circular cutouts for cords. The cutouts measured 3 inches in diameter. What is the approximate area of the desktop that Jamie sanded down?

2,261 square inches

Jana put a small triangular garden in a corner of her front yard. One side of the garden is 75 centimeters and another side is 78 centimeters. What is the area of the garden?

2,925 cm^2

Susy had a square plot of grass in her backyard, but now part of the plot is taken up by a fountain. Each side of the plot has a length of 14.5 feet. One side of the plot has a semicircular fountain with a radius of 2.5 feet. What is the approximate area of the plot of grass after installing the fountain?

200.4 ft.^2

A trapezoid has legs that are 13 cm and 15 cm long. The parallel sides are 11 cm and 25 cm long. The distance between the bases is 12 cm. What is the area of the trapezoid?

216 cm^2

Jason put new carpet in his bedroom. His bedroom is 15 feet by 14 feet. Along one 15-foot wall, a section is built out from the wall. That section is 8 feet by 2 feet. What is the area that Jason covered with carpet?

226 ft.^2

The city of Fauxtown is the shape of a trapezoid. The two legs have lengths of 16.5 miles and 15 miles. The two parallel sides have lengths of 13.5 miles and 19.5 miles and are 15 miles apart. How big is Fauxtown?

247.5 square miles

Dion makes and sells stained glass suncatchers in different shapes. For one of his designs, he attaches semicircles to each side of a square that has a side length of 4 centimeters. He builds a frame around the outside of each suncatcher to hold it together. What is the approximate length of the frame that Dion used on this suncatcher?

25.1 cm

Aliyah painted every surface of a block that is a rectangular prism with a cylindrical hole drilled through the center of the bases. The base edges of the prism are 2.5 inches and 2 inches, and the height of the block is 1.5 inches. The radius of the hole is 0.8 inches. What was the approximate area of the surface that Aliyah painted?

27 in.^2

A right square pyramid has a height of 15 centimeters. The length of the base is 40 centimeters. What is the surface area of the pyramid?

3,600 cm^2

Mateo needs to put sealant around a new window he is installing. The rounded window is made up of 5 squares that form a plus sign, and four quarter circles. The side length of each square is 3 inches. What is the approximate length of the sealant needed to go around the outside of the window?

30.8 inches

Derek cut a rubber ball in half to use for an art project. The diameter of the ball was 10.5 centimeters and the rubber was 1 centimeter thick. He covered the surface of one half of the ball with felt. This included the outside surface, the inside surface, and the 1 centimeter ring where he made the cut. What was the approximate area of the ball that Derek covered with felt?

316.5 cm ^2

A parallelogram has side lengths of 8 inches and 5 inches. The distance between the 8-inch sides is 4 inches. What is the area of the parallelogram?

32 in.^2

A candy company uses a special ball-shaped container to promote a new type of candy it wants to distribute. The diameter of the container is 4 inches. What is the approximate volume of the container?

33.5 in.^3

Examine the following prism. What is the volume of the prism?

36 cm^3

Aliyah drilled a cylindrical hole through the center of the bases of a wood block. The base edges of the block were 2.5 inches and 2 inches, and the height of the block was 1.5 inches. The radius of the hole was 0.8 inches. What is the approximate volume of the remaining wood block?

4.5 in.^3

What is the approximate perimeter of a semicircle with a diameter of 18 inches?

46.3 inches

A right cylinder has a radius of 7 feet and a height of 4 feet. What is the approximate surface area of the cylinder?

484 ft.^2

The diameter of a table tennis ball is 40 millimeters. What is the approximate surface area of a table tennis ball?

5,027 mm^2

Two lateral faces of a rectangular pyramid have a base length of 10 inches and a height of 15 inches. The other two lateral faces have a base length of 18 inches and a height of 13 inches. What is the surface area of the rectangular pyramid?

564 square inches

Susy has a square plot of grass in her backyard. Each side of the plot has a length of 14.5 feet. On one side, a semicircular fountain with a radius of 2.5 feet cuts into the plot of grass. She wants to put a brick border around the edge of the grass, so that it will also separate the grass from the fountain. What is the approximate length of the brick border?

60.9 feet

A rectangular pyramid has a height of 12 inches. The length of the pyramid's base is 18 inches, and the width of the base is 10 inches. What is the volume of the pyramid, rounded to the nearest whole number if necessary?

720 cubic inches

What is the approximate circumference of a circle with a radius of 13 feet?

81.7 feet

Examine the prism. What is the surface area of the prism?

84 cm^2

Molly is building a fence for her model of a proposed neighborhood dog park. The rectangular model is 20 inches by 26 inches. On one side of the park is a pond that needs to be fenced off. The part of the pond that cuts into the dog park is a semicircle, and on the model it has a radius of 2 inches. What is the approximate length of the fence on Molly's model?

94 inches

Use the following cone to answer the question. Which segment represents the height of the cone? (I can not put the line on top but there is a line on top.)

AB

What properties are true for all rectangles? Select all that apply.

All four angles are right angles. Opposite sides are parallel. Opposite sides are congruent.

Use the following prism to answer the question. Which segments are lateral edges? Select all that apply. (I can not put the line on top so I will just use the letter.)

CZ AX

Tasha is building a play pool with a small Jacuzzi in her backyard. The rectangular pool has a length of 16 feet and a width of 12 feet. The Jacuzzi is a semicircle with a radius of 4.5 feet that is attached on one side of the pool. She is going to put ceramic tiles along the top edge all the way around the pool and Jacuzzi. The tiles she wants to use cost $12.89 per foot, but she's not sure if this fits her budget. How can Tasha determine whether the tiles she wants fit her budget?

She can find the perimeter of a rectangle with the given dimensions and subtract the length where the semicircle is attached. Then she can add to the result the length of the semicircle. Then she can multiply this length by the cost of the tile and compare the result with her budget for the project

What property is true for all trapezoids?

The bases are parallel.

Match each net with the three-dimensional figure that correctly describes it.

The one that has all squares is a rectangular prism The one that has three squares and two triangles is a triangular prism The one that has a square in a middle and each side has a triangle is a rectangular pyramid The one that is a triangle and has a triangle in the center is a triangular pyramid

A company ships a package with identical spherical glass ornaments inside a rectangular box. The ornaments are protected by packing material that fills the box around the ornaments. To keep accurate records for shipping costs, the company needs to calculate the amount of packing material in the box. What formulas could the company use to determine how much packing material is in the box? Select all that apply.

V=4/3 πr3 V=Bh

Identify the parts shown in the figure of ⨀O. Match each part of the circle with the most specific term that describes it. (I can not put the half circle and line on top so it will be without it but everything is correct.)

WY with the half circle - semicircle WY with line - diameter XZ with line - chord XZ with half circle - arc OX with line - radius

Identify the parts shown in the figure of the trapezoid TRAP. Match each term with the correct part of the given trapezoid. (I can not put the line on top, but there is suppose to be line on top of each.)

height - ET leg - AR base - AP

Which units can be used to describe the perimeter of a shape?

kilometers miles inches

What units can be used to describe the area of a shape? Select all that apply.

square feet square meters

What units can be used to describe area? Select all that apply.

square meters square inches

What three-dimensional figure does the following net represent?

square pyramid

Which units can be used to describe the length of an object? Select all that apply.

yards meters