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Area and Volume

Math · Geometry and Trigonometry · 44 questions · every one comes with a full explanation.

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  1. 1A right circular cylinder has a volume of . If the height of the cylinder is 5, what is the radius of the cylinder?Medium · Geometry and Trigonometry
  2. 2Square A has side lengths that are 166 times the side lengths of square B. The area of square A is k times the area of square B. What is the value of k ?Hard · Geometry and Trigonometry
  3. 3The side length of a square is 55 centimeters cm. What is the area, in cm2, of the square?Easy · Geometry and Trigonometry
  4. 4What is the length of one side of a square that has the same area as a circle with radius 2 ?Medium · Geometry and Trigonometry
  5. 5Square X has a side length of 12 centimeters. The perimeter of square Y is 2 times the perimeter of square X. What is the length, in centimeters, of one side of square Y?Medium · Geometry and Trigonometry
  6. 6The area of a square is 64 square inches. What is the side length, in inches, of this square?Easy · Geometry and Trigonometry
  7. 7What is the volume, in cubic centimeters, of a right rectangular prism that has a length of 4 centimeters, a width of 9 centimeters, and a height of 10 centimeters?Medium · Geometry and Trigonometry
  8. 8A cube has an edge length of 68 inches. A solid sphere with a radius of 34 inches is inside the cube, such that the sphere touches the center of each face of the cube. To the neaHard · Geometry and Trigonometry
  9. 9The figure shown is a right circular cylinder with a radius of r and height of h . A second right circular cylinder (not shown) has a volume that is 392 times as large as the volHard · Geometry and Trigonometry
  10. 10A cube has an edge length of 41 inches. What is the volume, in cubic inches, of the cube?Medium · Geometry and Trigonometry
  11. 11A cylinder has a diameter of 8 inches and a height of 12 inches. What is the volume, in cubic inches, of the cylinder?Medium · Geometry and Trigonometry
  12. 12A manufacturing company produces two sizes of cylindrical containers that each have a height of 50 centimeters. The radius of container A is 16 centimeters, and the radius of contaMedium · Geometry and Trigonometry
  13. 13A rectangle has an area of 63 square meters and a length of 9 meters. What is the width, in meters, of the rectangle?Easy · Geometry and Trigonometry
  14. 14A cube has a volume of 474,552 cubic units. What is the surface area, in square units, of the cube?Hard · Geometry and Trigonometry
  15. 15A right circular cone has a height of 22 centimeters cm and a base with a diameter of 6 cm. The volume of this cone is nπ cm3. What is the value of n ?Hard · Geometry and Trigonometry
  16. 16A circle has a circumference of 31π centimeters. What is the diameter, in centimeters, of the circle?Medium · Geometry and Trigonometry
  17. 17A manufacturer determined that right cylindrical containers with a height that is 4 inches longer than the radius offer the optimal number of containers to be displayed on a shelf.Hard · Geometry and Trigonometry
  18. 18Triangle ABC and triangle DEF are similar triangles, where and are corresponding sides. If and the perimeter of triangle ABC is 20, what is the perimeter of triangle DEF ?Easy · Geometry and Trigonometry
  19. 19A rectangular poster has an area of 360 square inches. A copy of the poster is made in which the length and width of the original poster are each increased by 20 %. What is the arHard · Geometry and Trigonometry
  20. 20A right rectangular prism has a length of 28 centimeters cm, a width of 15 cm, and a height of 16 cm. What is the surface area, in cm2, of the right rectangular prism?Hard · Geometry and Trigonometry
  21. 21What is the area, in square centimeters, of a rectangle with a length of 34 centimeters cm and a width of 29 cm?Easy · Geometry and Trigonometry
  22. 22A right circular cone has a volume of cubic feet and a height of 9 feet. What is the radius, in feet, of the base of the cone?Hard · Geometry and Trigonometry
  23. 23A rectangle has a length of 13 and a width of 6 . What is the perimeter of the rectangle?Easy · Geometry and Trigonometry
  24. 24A triangular prism has a height of 8 centimeters cm and a volume of 216 cm3. What is the area, in cm2, of the base of the prism? (The volume of a triangular prism is equal to B Medium · Geometry and Trigonometry
  25. 25The lengths of the sides are x, y, and z. A note indicates the figure is not drawn to scale. The triangle shown has a perimeter of 22 units. If x=9 units and y=7 units, what iEasy · Geometry and Trigonometry
  26. 26What is the area, in square centimeters, of a rectangle with a length of 36 centimeters and a width of 34 centimeters?Easy · Geometry and Trigonometry
  27. 27Two identical rectangular prisms each have a height of 90 centimeters cm. The base of each prism is a square, and the surface area of each prism is K cm2. If the prisms are glued tHard · Geometry and Trigonometry
  28. 28The volume of right circular cylinder A is 22 cubic centimeters. What is the volume, in cubic centimeters, of a right circular cylinder with twice the radius and half the height ofHard · Geometry and Trigonometry
  29. 29The area of a rectangle is 630 square inches. The length of the rectangle is 70 inches. What is the width, in inches, of this rectangle?Easy · Geometry and Trigonometry
  30. 30What is the area of a rectangle with a length of 17 centimeters cm and a width of 7 cm?Easy · Geometry and Trigonometry
  31. 31Moving from left to right, the points have the following coordinates: (negative 3 comma 4) (4 comma negative 3) (5 comma 3) What is the area, in square units, of the triangle forHard · Geometry and Trigonometry
  32. 32Circle A has a radius of 3 n and circle B has a radius of 129 n , where n is a positive constant. The area of circle B is how many times the area of circle A ?Hard · Geometry and Trigonometry
  33. 33Each side of a square has a length of 45 . What is the perimeter of this square?Easy · Geometry and Trigonometry
  34. 34What is the area of a rectangle with a length of 4 centimeters cm and a width of 2 cm?Easy · Geometry and Trigonometry
  35. 35A rectangle has a length of 64 inches and a width of 32 inches. What is the area, in square inches, of the rectangle?Easy · Geometry and Trigonometry
  36. 36The dimensions of a right rectangular prism are 4 inches by 5 inches by 6 inches. What is the surface area, in square inches, of the prism?Hard · Geometry and Trigonometry
  37. 37The figure shows the lengths, in centimeters (cm), of the edges of a right rectangular prism. The volume V of a right rectangular prism is , where is the length of the prism, w is Easy · Geometry and Trigonometry
  38. 38A cylindrical can containing pieces of fruit is filled to the top with syrup before being sealed. The base of the can has an area of , and the height of the can is 10 cm. If of syrMedium · Geometry and Trigonometry
  39. 39A right triangle has sides of length 2 2 , 6 2 , and 80 units. What is the area of the triangle, in square units?Hard · Geometry and Trigonometry
  40. 40The glass pictured above can hold a maximum volume of 473 cubic centimeters, which is approximately 16 fluid ounces. What is the value of k, in centimeters?Medium · Geometry and Trigonometry
  41. 41What is the perimeter, in inches, of a rectangle with a length of 4 inches and a width of 9 inches?Easy · Geometry and Trigonometry
  42. 42Triangles ABC and DEF are similar. Each side length of triangle ABC is 4 times the corresponding side length of triangle DEF. The area of triangle ABC is 270 square inches. What Hard · Geometry and Trigonometry
  43. 43A cube has a surface area of 54 square meters. What is the volume, in cubic meters, of the cube?Hard · Geometry and Trigonometry
  44. 44In the xy-plane shown, square ABCD has its diagonals on the x- and y-axes. What is the area, in square units, of the square?Medium · Geometry and Trigonometry