Which of the following statements best describes an attribute of a right rectangular prism?(1 point)
Responses
It has two identical parallel bases and two rectangular lateral faces.
It has two identical parallel bases and two rectangular lateral faces.
It has two identical, parallel rectangular bases and four rectangular lateral faces.
It has two identical, parallel rectangular bases and four rectangular lateral faces.
It is rectangular and therefore has four edges.
It is rectangular and therefore has four edges.
Its vertices meet at 45-degree angles.
2. What type of pyramid has attributes that include 5 faces: 4 lateral faces that are triangles and meet at an apex and a base that is square?(1 point)
Responses
square pyramid
square pyramid
triangular pyramid
triangular pyramid
irregular pyramid
irregular pyramid
pentagonal pyramid
3. Define surface area.(1 point)
Responses
Surface area is the total amount around an object.
Surface area is the total amount around an object.
Surface area is half the amount of space on a net.
Surface area is half the amount of space on a net.
Surface area is the amount of space an object takes up.
Surface area is the amount of space an object takes up.
Surface area is the sum of the areas of all faces of a three-dimensional object.
4. What is wrong in this calculation of the surface area? SA=(wl + lh + hw)
𝑆
𝐴
=
(
𝑤
𝑙
+
𝑙
ℎ
+
ℎ
𝑤
)
(1 point)
Responses
The formula is correct.
The formula is correct.
The contents of the parentheses need to be squared.
The contents of the parentheses need to be squared.
The contents of the parentheses must be multiplied by 2.
The contents of the parentheses must be multiplied by 2.
The order of the multiplication is wrong.
5. Use the image to answer the question.An illustration shows a 3 D box with length of 36 inches labeled as front, a width of 28 inches, and height of 25 inches. A line on either side of the box runs along the length of the top and front. The space between the line and the edge of the box is labeled 3 inches on each side. The trim (shaded area) around the edge of a trunk needs to be painted. If the trim is painted all the way around, what is the surface area to be painted?
636 in.2
636
in.
2
636 in. squared
318 in.2
318
in.
2
318 in. squared
5,216 in.2
5
,
216
in.
2
5,216 in squared
1,400 in.^2
6. Find the surface area of a rectangular pyramid with these measurements: l
𝑙
= 5.5 yd., w
𝑤
= 4 yd., and h
ℎ
= 6 yd. (1 point)
Responses
255.06 yd.2
255.06
yd.
2
255 point 0 6 yards squared
242.27 yd.2
242.27
yd.
2
242 point 2 7 yards squared
83.19 yd.2
83.19
yd.
2
83 point 1 9 yards squared
56.79 yd.^2
7. What is the surface area of a square pyramid if the base edge = 68 in. and the slant height = 125 in.?(1 point)
Responses
21,624 in2
21
,
624
in
2
21,624 in squared
17,068 in2
17
,
068
in
2
17,068 in squared
17,000 in2
17
,
000
in
2
17,000 in squared
32,625 in^2
8. What is the surface area of a square pyramid where the length of the base edge is 20 cm and the height is 26 cm? Round your answer to the nearest whole number.(1 point)
Responses
1,114 cm2
1
,
114
cm
2
1 comma 114 cm squared
1,440 cm2
1
,
440
cm
2
1 comma 440 cm squared
1,514 cm2
1
,
514
cm
2
1 comma 514 cm squared
1,134 cm^2
9. Find the surface area of a triangular pyramid with base 10, a base height of 8.7, and a slant height of 12.(1 point)
Responses
216.6
216.6
103.5
103.5
223.5
223.5
232.2
10. An architect is designing a glass greenhouse in the form of a triangular pyramid for the botanical gardens. Find the surface area of the triangular pyramid with a base of 100 ft., a base height of 86.6 ft., and a slant height of 120 ft.(1 point)
Responses
21,660 ft.2
21
,
660
ft.
2
21,660 ft. squared
10,350 ft.2
10
,
350
ft.
2
10,350 ft. squared
22,330 ft.2
22
,
330
ft.
2
22,330 ft. squared
23,220 ft.^2
11. What is the volume of a right rectangular prism with a length of 6, width of 5, and height of 8?(1 point)
Responses
19
19
24
24
240
240
80
12. Andres needs to fill a swimming pool. The pool is in the shape of a rectangular prism. The pool has a width of 9 feet, a length of 12 feet, and a depth of 7 feet. What is the volume of the pool?(1 point)
Responses
756 cubic feet
756 cubic feet
28 cubic feet
28 cubic feet
252 cubic feet
252 cubic feet
763 cubic feet
13. A box is being constructed in the shape of a right rectangular prism. What is the volume of the box when the length is 25 inches, the width is 15 inches, and the height is 5 inches?(1 point)
Responses
1,750 cubic inches
1,750 cubic inches
200 cubic inches
200 cubic inches
1,875 cubic inches
1,875 cubic inches
45 cubic inches
14. What is the volume of a rectangular pyramid with a width of 9 cm, a length of 15 cm, and an altitude of 21 cm?(1 point)
Responses
2,835 cm3
2
,
835
cm
3
2,835 cm cubed
8,505 cm3
8
,
505
cm
3
8,505 cm cubed
945 cm3
945
cm
3
945 cm cubed
15 cm^3
15. Lena is looking for a new tent to go camping. She wants one with a volume of at least 200 cubic feet. The tent she is considering is 8 feet tall with a base of 8 feet by 8 feet. Will this tent have a large enough volume?(1 point)
Responses
Yes, the volume is 512 ft3
512
ft
3
.
Yes, the volume is 512 ft cubed .
No, the volume is only 24 ft3
24
ft
3
.
No, the volume is only 24 ft cubed .
Yes, the volume is 1,536 ft3
1
,
536
ft
3
.
Yes, the volume is 1,536 ft cubed .
No, the volume is only 170.67 ft^3
170.67
ft
3
.
3 answers
Here are the answers to your questions based on the given statements:
Which of the following statements best describes an attribute of a right rectangular prism?
It has two identical, parallel rectangular bases and four rectangular lateral faces.
What type of pyramid has attributes that include 5 faces: 4 lateral faces that are triangles and meet at an apex and a base that is square?
square pyramid
Define surface area.
Surface area is the sum of the areas of all faces of a three-dimensional object.
What is wrong in this calculation of the surface area? SA=(wl + lh + hw)
The contents of the parentheses must be multiplied by 2.
Use the image to answer the question. If the trim is painted all the way around, what is the surface area to be painted?
636 in.²
Find the surface area of a rectangular pyramid with these measurements: l = 5.5 yd., w = 4 yd., and h = 6 yd.
242.27 yd.²
What is the surface area of a square pyramid if the base edge = 68 in. and the slant height = 125 in.?
21,624 in²
What is the surface area of a square pyramid where the length of the base edge is 20 cm and the height is 26 cm? (Round to the nearest whole number.)
1,134 cm²
Find the surface area of a triangular pyramid with base 10, a base height of 8.7, and a slant height of 12.
223.5
An architect is designing a glass greenhouse in the form of a triangular pyramid. Find the surface area of the triangular pyramid with a base of 100 ft., a base height of 86.6 ft., and a slant height of 120 ft.
21,660 ft.²
What is the volume of a right rectangular prism with a length of 6, width of 5, and height of 8?
240
Andres needs to fill a swimming pool. The pool has a width of 9 feet, a length of 12 feet, and a depth of 7 feet. What is the volume of the pool?
756 cubic feet
A box is being constructed in the shape of a right rectangular prism. What is the volume of the box when the length is 25 inches, the width is 15 inches, and the height is 5 inches?
1,875 cubic inches
What is the volume of a rectangular pyramid with a width of 9 cm, a length of 15 cm, and an altitude of 21 cm?
2,835 cm³
Lena is looking for a new tent to go camping. She wants one with a volume of at least 200 cubic feet. The tent she is considering is 8 feet tall with a base of 8 feet by 8 feet. Will this tent have a large enough volume?
Yes, the volume is 512 ft³.
Feel free to ask if you need further clarifications or assistance!
6. 83.19 yd.^2
14. 945 cm^3
15. No, the volume is only 170.67 ft^3
Let's clarify the answers for questions 6, 14, and 15 based on the provided options and calculations:
6. Find the surface area of a rectangular pyramid with these measurements: l = 5.5 yd., w = 4 yd., and h = 6 yd.
The surface area of a rectangular pyramid can be calculated using the formula:
\[
\text{SA} = lw + \frac{1}{2} \times \text{perimeter of the base} \times \text{slant height}
\]
Given the values:
Length (l) = 5.5 yd
Width (w) = 4 yd
Height (h) = 6 yd (but we need the slant height, which will need calculating based on the triangle formed).
The provided answer of 83.19 yd² does not seem correct unless there's a specific calculation to support it.
Hence, I suggest double-checking the work based on formulas.
14. What is the volume of a rectangular pyramid with a width of 9 cm, a length of 15 cm, and an altitude of 21 cm?
The volume \( V \) of a rectangular pyramid is calculated via the formula:
\[
V = \frac{1}{3} \times \text{base area} \times \text{height}
\]
Base area = length × width = \( 15 , \text{cm} \times 9 , \text{cm} = 135 , \text{cm}^2 \)
Height = 21 cm
Thus,
\[
V = \frac{1}{3} \times 135 , \text{cm}^2 \times 21 , \text{cm} = 945 , \text{cm}^3
\]
So, your selection of 945 cm³ is correct!
15. Lena is looking for a new tent to go camping. She wants one with a volume of at least 200 cubic feet. The tent she is considering is 8 feet tall with a base of 8 feet by 8 feet. Will this tent have a large enough volume?
To find the volume \( V \) of the tent:
\[
V = \text{base area} \times \text{height}
\]
Base area = \( 8 , \text{ft} \times 8 , \text{ft} = 64 , \text{ft}^2 \)
Height = 8 ft
So,
\[
V = 64 , \text{ft}^2 \times 8 , \text{ft} = 512 , \text{ft}^3
\]
Therefore, the correct answer is Yes, the volume is 512 ft³.
The response suggesting "No, the volume is only 170.67 ft³” is incorrect. The tent does indeed have a sufficient volume for her needs.
Please ensure you check the calculations against the right formulas, and let me know if you have further inquiries!
