Perimeter, Area, Volume

Other Shapes

Tisha is building a wooden drying rack. The top of the rack is in the shape of a trapezoid. The trapezoid's bases are 24 inches long and 38 inches long, respectively. Tisha will add a brace that joins the midpoints of the trapezoid's 2 nonparallel sides to support her drying rack, as shown in the figure below. How many inches long will the brace be?

2023 September(G01) Math Question 1

2019 June(72F) Math Question 5

5. A formula for the volume of a right circular cone is

2017 June(74C) Math Question 5

What is the volume, in cubic inches, of a sphere with a diameter of 10 inches? (Note: The volume, V, of a sphere with radius r is given by the formula V = (4/3)πr³.)

2023 April(F11) Math Question 9

The dimensions of a hallway floor are shown below. Each pair of adjacent walls meets at a right angle. Teresa plans to completely carpet this entire hallway floor. At a cost of $2 per square foot, how much will carpeting this hallway floor cost?

2023 September(G01) Math Question 13

14. The volume of a sphere is 41c3r , where r is the radius
of the sphere. What is the volume, in cubic yards, of a sphere with a diameter of 4 yards?

2018 June(A11) Math Question 14

14. An ellipse with a major axis of length 6 inches and a minor axis of length 4 inches is inscribed in a rectangle, as shown below. The region inside the rectangle but outside the ellipse is shaded. What is the area, in square inches, of the shaded region? (Note: The area, A, of any ellipse can be found by the formula A = πab where a is the length of the major axis and b is the length of the minor axis.)

Area of Ellipse

2020 December(D03) Math Question 14

2011 June(69F) Math Question 15

16. The perimeter of a parallelogram is 80 inches, and the length of 1 side is 16 inches. If it can be determined, what are the lengths, in inches, of the other 3 sides?

2015 December(72E) Math Question 16

The circular region containing the track and the infield (the grassy region enclosed by the track) is divided into sectors that each have a central angle of 60°. Each sector is a different color. What is the area, in square meters, of each sector?

35 February(Z14) Math Question 16

The following shapes are a circle and some regular polygons that have their centers marked. All units are given in feet. Which of these shapes has the greatest area?

2024 April(Z13) Math Question 16

2009 June(67C) Math Question 17

The area of the trapezoid shown below is 20 square feet, the height is 5 feet, and the length of one base is 2 feet. What is b, the length of the other base, in feet?

35 February(Z14) Math Question 18

20. The perimeter of a parallelogram is 80 inches, and the length of 1 side is 18 inches. If it can be determined, what are the lengths, in inches, of the other 3 sides?

2014 April(71H) Math Question 20

23. The perimeter of a parallelogram is 76 inches, and the length of 1 side is 10 inches. If it can be determined, what are the lengths, in inches, of the other 3 sides?

2014 December(72G) Math Question 23

2019 June(72F) Math Question 23

A machine blade in the shape of a right triangle is rotated about a mechanical shaft at high speed. The mechanical shaft is along the longer leg of the triangle that represents the blade. One of the following solids is generated as the blade rotates about the shaft. Which one?

2024 September(H11) Math Question 23

24. A parallelogram has a perimeter of 84 inches, and 1 of its sides measures 16 inches. If it can be determined, what are the lengths, in inches, of the other 3 sides?

2017 June(74C) Math Question 24

24. To the nearest 1 foot, what is the heig~t of a rectangular
prism with a base length of 15 feet, a base width of
1 ½ feet, and a volume of 100 cubic feet?

2019 June(B02) Math Question 24

A certain right circular cone has a volume of 616 cubic meters. Given that the cone has a height of 5 meters, which of the following gives the radius of the base of the cone, in meters?

2024 December(H31) Math Question 24

The table below gives the lengths, widths, and heights, in feet, of 3 right rectangular prisms. The difference between the volume of Prism A and the volume of Prism B is how many times the volume of Prism C?

2024 April(Z13) Math Question 26

2011 April(67F) Math Question 27

A small hole was torn in the bottom corner of an unopened 1.5-pound bag of granulated sugar. By the time the hole was plugged, the leaked sugar had formed a pile in the shape of a cone with a radius of 3 inches and a height of 2 inches. Given that granulated sugar weighs 0.025 pounds per cubic inch, which of the following values is closest to the amount of sugar, in pounds, that was left in the bag after the leak was fixed? (Note: The volume of a cone with radius r and height h is given by V = (1/3)πr²h.)

2025 October(J08) Math Question 27

29. What is the area, in square coordinate units, of ABCD ?

2017 June(74C) Math Question 29

2019 December(C03) Math Question 30

2010 April(68G) Math Question 30

2020 June(C02) Math Question 30

Jerry will use bags of concrete mix to make the step. Each bag makes 0.4 cubic feet of concrete. To the nearest 0.1 bag, how many bags of concrete mix will he need for the step?

35 February(Z14) Math Question 31

Rafael wrapped a gift box l inches long, w inches wide, and h inches high. He tied a decorative rope around it and used an extra 6 inches for a tie at the top, as shown below. On both the top and the bottom, he formed right angles where the rope crossed. About how many inches of decorative rope did Rafael use?

2023 September(G01) Math Question 32

2011 April(67F) Math Question 33

A piece of chocolate candy enclosing an almond in the center is made in a rectangular mold that has inside dimensions 4 cm, 3 cm, and 2 cm. If the volume of the almond is 2 cubic centimeters, what is the maximum volume, in cubic centimeters, of the chocolate in the piece of candy?

2023 September(G01) Math Question 33

2010 June(68C) Math Question 35

2020 June(C02) Math Question 35

36. The solid shown below is composed of a right circular cylinder and a right circular cone with base diameters and heights given in centimeters. The cylinder and the cone have equal base diameters. What is the volume, in cubic centimeters, of the solid?

2014 June(72C) Math Question 36

2011 April(67F) Math Question 36

2020 July(C01) Math Question 36

2011 June(69F) Math Question 38

2010 December(69A) Math Question 39

2010 June(68C) Math Question 39

Which of the following 2-dimensional shapes, when rotated about its vertical symmetry line, will form the shape of this lampshade?

2024 June(G20) Math Question 39

40. A sphere with radius x inches has a volume of 12 cubic inches. What is the value of x ? (Note: The volume of a sphere with radius r is 4/3 Pi r^3.)

2015 June(73C) Math Question 40

2009 December(68A) Math Question 40

2010 April(68G) Math Question 41

A wheel with a radius of 1 centimeter rolls without slipping along the ground. After exactly 2 revolutions, how many centimeters has the wheel traveled along the ground?

35 February(Z14) Math Question 41

42. Which of the following vertical lines cuts ABCD into 2 trapezoids with equal areas?

2014 June(72C) Math Question 42

2010 December(69A) Math Question 42

Rectangular pyramids A (left) and B (right) are shown below with dimensions given in feet. Let a and b be the volumes of A and B, respectively. Which of the following equations is true?

2024 June(G20) Math Question 42

2009 April(66F) Math Question 43

A net of a square pyramid with 4 congruent triangular sides is shown below in the standard (x,y) coordinate plane. Points A, B, and C are vertices of the net. What is the total surface area, in square coordinate units, of the pyramid?

2024 December(H31) Math Question 43

2013 April(71G) Math Question 46

2013 April(71G) Math Question 47

2010 April(68G) Math Question 47

47. The volume of a solid object is equal to the volume of water it displaces when completely submerged in water. A solid object will be placed in a rectangular tank that has a base of 35 cm by 30 cm and is filled with water to a uniform depth of 13 cm. When the object is completely submerged, the new depth of the water in the tank is 15 cm. What is the volume, in cubic centimeters, of the object?

2021 June(D06) Math Question 47

47. The right semicircular cylinder shown below has a height of 5 centimeters and a semicircular base of radius 3 centimeters. What is the volume, in cubic centimeters, of the right semicircular cylinder?

Cylinders

2021 April(D05) Math Question 47

49. In trapezoid ABCD illustrated below, AB is 8 units long, CD is 12 units long, and EF is 6 units long. Also, ZAEF and LDFE are right angles, What is the area of ABCD, in square units?

2015 December(72E) Math Question 49

2010 December(69A) Math Question 49

49. What is the area, in square inches, of the parallelogram shown below?

2015 April(73G) Math Question 49

2012 December(71A) Math Question 50

2009 December(68A) Math Question 50

50. If the area of KLMN in the figure below is 12 square centimeters, what is the length, in centimeters, of LM ?

2015 June(73C) Math Question 50

50. A right prism with triangular bases and with dimensions given in inches is shown below. What is the prism’s total surface area, in square inches?

2014 April(71H) Math Question 50

50. The radius and height of the right circular cylinder shown below are given in centimeters. Which of the following is closest to the volume, in cubic centimeters, of the cylinder?

2014 December(72G) Math Question 50

51. The volume of a right circular cone with radius r and height h is 1/3 pi r^2h, where r and h have the same unit of measure. Cones A and B are both right circular cones. The radius of Cone B is 2 times the radius of Cone A. Cone B's height is 1/2 Cone A's height. Compared to the volume of Cone A, the volume of Cone B is:

2016 April(73E) Math Question 51

51. In the figure below, the side lengths and the length of an altitude of parallelogram BCDE are given in feet. What is the area, in square feet, of BCDE ?

2014 June(72C) Math Question 51

52. A can of soda pop has the shape of a right circular cylinder with an inside height of 6 inches and an inside diameter of 2 inches. When you pour the soda pop from the full can into a cylindrical glass with an inside diameter of 3 inches, about how many inches high is the soda pop in the glass? (Note: The volume of a right circular cylinder is itr2h.)

2015 April(73G) Math Question 52

The interior diameter and interior height of a cylindrical container are given in inches in the figure below. Water will be poured into the empty container at a rate of 40π cubic inches per minute. At this rate, in exactly how many minutes will the container be completely filled?

2024 September(H11) Math Question 52

2012 June(70C) Math Question 55

2012 April(70G) Math Question 56

2011 June(69F) Math Question 57

2013 April(71G) Math Question 57

The base of a right square pyramid has a side length of 20 ft. The pyramid's slant height is 15 ft. What is the total surface area, in square feet, of the pyramid?

2024 April(Z13) Math Question 57

58. As shown below, BE divides rectangle ACDF into 2 congruent trapezoids. The measure of BED is 45°. The lengths of BC, CD, and EF are given in feet. What is the area, in square feet, of rectangle ACDF ?

2015 December(72E) Math Question 58

59. The plans for a diving pool call for a rectangular prism that has a length of 30 meters, a width of 25 meters, and a depth of 5 meters. If the plans are changed to increase both the length and the width of the pool by 10%, what will be the increase, to the nearest 1%, in the volume of the pool?

2017 December(A10) Math Question 59

A solid rectangular block of steel weighs w pounds. Which of the following expressions gives the weight, in pounds, of a larger solid rectangular block that is made of the same kind of steel and has length, width, and height 4 times those of the smaller block?

Other ShapesPerimeter, Area, VolumeACT math questions

2023 September(G01) Math Question 1

2019 June(72F) Math Question 5