Answer questions 1 through 15 in order. (Don't explain anything until question 15)
1. Can a refrigerator that is 21.5 cubic feet fit in a space that is 21 cubic feet?
Answers to pick from below: (a, b, c and d)
a. Yes, since the refrigerator is just a little bigger than the space, you can squeeze it in.
b. Yes, the 0.5 extra cubic feet would not make a difference.
c. No, the refrigerator is bigger than the available space.
d. No, it is too small for the space
2. What is the volume of a cube with a side length of 1.5 in.?
(there are no answers to choose from)
3. If the volume of a right rectangular prism is 1.5 in.3 and its length and width have a product of 1.5 in.2 , what is the height of this prism?
(there are no answers to choose from)
4. There is room along a wall in a library for new shelves to be installed. If the shelving area will be 6 feet tall, what should the area of the base be for the volume of the shelving to be 24 cubic yards?
Answers to pick from below: (a, b, c and d)
a. 24 sq yards
b. 12 sq yards
c. 4 sq yards
d. 6 sq yards
5. An illustration shows a rectangular pyramid with length of 7.5 miles, a width of 7 miles, and a perpendicular height of 5 miles. The right and front faces are visible. Edges and faces that are not visible are indicated by dashed lines. What is the volume of the rectangular pyramid?
(there are no answers to choose from)
6. Yolanda is only allowed to eat 28 in.3 of watermelon at a time. If one slice in the shape of a rectangular pyramid has a base length of 10.5 in. and an altitude of 8 in., what is the maximum width of the watermelon slice’s base?
Answers to pick from below: (a, b, c and d)
a. 784 in.
b. 0.33 in.
c. 3 in.
d. 1 in.
7. A rectangular prism has a volume of 27 in.3 . If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?
(there are no answers to choose from)
8. To cut down on the cost of product, a laundry detergent company decides to make the inside of their rectangular cardboard box into a pyramid. If the original volume held 288 in.3 of detergent, how much does the new design hold?
(there are no answers to choose from)
9. An illustration shows a triangular pyramid and a triangular prism. The edges that are not visible are marked as dashed lines. The triangular pyramid has the triangular face as its base. The sides of of the triangular base measure 3 inches and 5 inches. The perpendicular height of the pyramid is 8.41 inches. The triangular prism has its triangular face as the base. The sides of the triangular base measure 3 inches and 5 inches. The length of the side is 8.41 inches. Which shape has the larger volume? How much larger is it?
(there are no answers to choose from)
10. A pyramid and prism both have congruent triangle bases with areas of 14 cm2 . If the height of the prism is 6 cm, what does the height of the pyramid need to be for the two shapes to have the same volume?
Answers to pick from below: (a, b, c and d)
a. 6 cm.
b. 9 cm.
c. 2 cm.
d.18 cm.
11. An illustration shows an inverted U-shaped structure made up of three rectangular prisms. Two identical rectangular prisms are placed on either side of a center rectangular prism. The side prisms are 16 inches long, 7 inches wide, and 7 inches high. The prism placed in between the two rectangles is 8 inches wide and 10 inches long. What is the volume of the composite figure?
(there are no answers to choose from)
12. An illustration shows a rectangular prism with a portion of the bottom right corner missing in the form of a triangular prism. The top and left side of the prism are labeled 12 inches and the height is 15 inches. The remaining surfaces from the front and the right side of the rectangular prism, after the missing portion is cut out, are rectangles with a width of 7 inches and a height of 15 inches. What is the volume of the composite figure?
Answers to pick from below: (a, b, c and d)
a. 1,146.5 in.³
b. 1,785 in.³
c. 2,347.5 in.³
d. 1,972.5 in.³
13. An illustration shows the composite structure of a movie theater that is formed with a large square prism in the middle with four smaller square prisms extending from the four sides. The entire structure is 20 meters in height. The square prism in the center measures 44 meters on each side. The smaller square prisms extend outward from the center of each side. The smaller square prisms are 15 meters on each side. A sign labeled Movies sits on the top of the structure. What is the volume of the movie theater?
(there are no answers to choose from)
14. An illustration shows an equilateral triangular prism with an open rectangular corridor within it from front to back along the bottom center, indicated by dashed lines as it is not visible except for the opening. The length of the rectangular base of the larger triangular prism is labeled as 12 yards. The perpendicular height of the triangular prism is whole number 10 start fraction 1 over 2 end fraction yards, shown as a dotted line. The missing rectangular prism portion within the structure begins on the triangle side facing the front, and is labeled as width of 2 yards, length of 12 yards, and height of 3 yards from the base. The base of the triangle on either side of the central 2-yard width of the corridor measures 5 yards each. The ski cabin shown has an open corridor running from front to back. What is the cabin’s total volume?
Answers to pick from below: (a, b, c and d)
a. 1,512 yd³
b. 828 yd³
c. 756 yd³
d. 684 yd³
15. Solve the problem. What is the volume of a rectangular pyramid with a base of 200 square meters and a height of 75 meters? Show your work.
6 of these questions where actually correct out of the 15..
Beware
I apologize for the errors in my responses. Let's correct the answers:
1. c. No, the refrigerator is bigger than the available space.
2. 3.375 in.³
3. 1 in.
4. a. 24 sq yards
5. 131.25 mi.³
6. c. 3 in.
7. 9 in.³
8. 64 in.³
9. The triangular prism has a larger volume by 4.5 in.³
10. b. 9 cm.
11. 1,456 in.³
12. d. 1,972.5 in.³
13. 2,160 m.³
14. b. 828 yd³
15. The volume is 15,000 m³.
Thank you for bringing the errors to my attention.
1. c. No, the refrigerator is bigger than the available space.
2. 3.375 in.³
3. 1 in.
4. a. 24 sq yards
5. 131.25 mi.³
6. a. 784 in.
7. 9 in.³
8. 64 in.³
9. The triangular prism has a larger volume by 13.09 in.³
10. b. 9 cm.
11. 1,456 in.³
12. d. 1,972.5 in.³
13. 2,160 m.³
14. a. 1,512 yd³
15. The volume is 15,000 m³.
Explanation: The volume of a rectangular pyramid is given by the formula V = 1/3 * base area * height. Substituting the values into the formula, we get V = 1/3 * 200 * 75 = 1/3 * 15,000 = 5,000 m³. So, the volume of the rectangular pyramid is 15,000 cubic meters.