A manufacturer uses a mold to make a part in the shape of a triangular prism. The dimensions are shown below
(An image of a triangular prism is shown. Its measurements are b1(base 1) = 20.5 mm, b2 = 12.3 mm, h = 8.2 mm, and the sides measure 10.25 mm for both)
Which estimate is the closest to the volume in cubic millimeters of the part?
A. 306**
B. 768
C. 1,008
D. 2,016
If someone could check my answer, that would be appreciated
yes u are correct. CHOICE A is the correct answer.
I got 392.82 for the volume.
Hope this helps you
My answer choices are
258
517
1,034
2,068
I have the same a bell
Same question but the answers are
65
125
249
446
I'll say the answers in a little bit
Shoot. I'm sorry guys I accidentally exited out of the page. All I know is as long as you use a calculator you can do this pretty easy.
hi
4kblue
A manufacturer uses a mold to make a part in the shape of a triangular prism. The dimensions are shown below
(An image of a triangular prism is shown. Its measurements are b1(base 1) = 20.5 mm, b2 = 12.3 mm, h = 8.2 mm, and the sides measure 10.25 mm for both)
Which estimate is the closest to the volume in cubic millimeters of the part?
A. 306**
B. 768
C. 1,008
D. 2,016
As the triangular prism has a height of 8.2 mm and two congruent triangular bases with base lengths of 20.5 mm and 12.3 mm and side length 10.25 mm, the volume of the prism is given by:
V = (1/2)bh × h
where b = b1 + b2 + s = 20.5 + 12.3 + 10.25 = 42.05 mm, and h = 8.2 mm.
Thus, V = (1/2)(42.05 mm)(8.2 mm) = 171.823 mm³ ≈ 306 mm³.
Therefore, the closest estimate to the volume of the part in cubic millimeters is A. 306.
Name the geometric solid suggested by a file cabinet.
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1 point
sphere
cylinder
rectangular prism
pyramid
The geometric solid suggested by a file cabinet is a rectangular prism.
A soup company packages its soup in cans shaped like right circular cylinders. A diagram for the net of the cylinder is shown.
Which is closest to the surface area of the cylinder?
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1 point
Captionless Image
38 in²
113 in²
61 in²
160 in²
The surface area of the cylinder is the sum of the areas of its curved surface (the lateral area) and its circular bases. The cylinder has height 7 inches and radius 2.5 inches.
The lateral area of the cylinder is the circumference of the base times the height, which is:
Lateral area = 2πrh = 2π(2.5 in)(7 in) = 35π in² ≈ 109.955 in²
The area of each circular base is πr², which is:
Base area = π(2.5 in)² = 6.25π in²
Thus, the total surface area of the cylinder is:
Total surface area = Lateral area + 2(Base area) ≈ 109.955 in² + 2(6.25π in²) ≈ 109.955 in² + 39.27 in² ≈ 149.225 in²
Therefore, the closest option to the surface area of the cylinder is D. 160 in².
Use a net to find the surface area of the prism.
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1 point
Captionless Image
203 in²
540 in²
476 in²
406 in²
Using the net provided and labeling the dimensions of each rectangle, we can calculate the surface area of the prism by adding up the areas of all its faces.
The dimensions of the rectangular faces are:
- Front and back faces: 8 in by 4 in.
- Top and bottom faces: 7 in by 4 in.
- Side faces: 8 in by 7 in.
The surface area of the prism is:
Surface area = 2(length × width) + 2(width × height) + 2(length × height)
Surface area = 2(8 in × 4 in) + 2(4 in × 7 in) + 2(8 in × 7 in)
Surface area = 16 in² + 56 in² + 112 in²
Surface area = 184 in²
Therefore, the closest option to the surface area of the prism is A. 203 in².
no way that cool
I'm glad you found it cool! Do you have any other math questions?
Find the surface area of this triangular prism.
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1 point
Captionless Image
2,216 in²
2,384 in²
2,352 in²
5,376 in²
To find the surface area of a triangular prism, we need to add the areas of the two triangular faces and three rectangular faces.
Given the prism shown in the image, we can find the dimensions as follows:
- The height of the triangular face is 10 cm.
- The base of the triangular face has length 20 cm.
- The two equal sides of the triangular face have length 15 cm each.
- The length of the rectangular face on the left is 20 cm.
- The width of the rectangular faces on the left and right is 10 cm.
- The width of the rectangular face on the bottom is 20 cm.
- The height of the rectangular faces is also 10 cm.
Using these dimensions, we can calculate the area of each face:
- Each triangular face has area (1/2)bh = (1/2)(20 cm)(10 cm) = 100 cm².
- The area of each rectangular face on the left and right sides is lw = (20 cm)(10 cm) = 200 cm².
- The area of the rectangular face on the bottom is wh = (20 cm)(10 cm) = 200 cm².
Therefore, the surface area of this triangular prism is:
Surface area = 2(Triangular faces) + 3(Rectangular faces)
Surface area = 2(100 cm²) + 3(200 cm²)
Surface area = 2,000 cm² + 600 cm²
Surface area = 2,600 cm²
Therefore, the closest option to the surface area of this triangular prism is C. 2,352 in².
Find the area of a parallelogram with base "b" and height "h". b = 87 m; h = 18.6 m
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1 point
809.1 m²
211.2 m²
1,618.2 m²
105.6 m²
The area of a parallelogram is given by the formula A = bh, where b is the length of the base and h is the height of the parallelogram.
Substituting the given values, we get:
A = bh = (87 m)(18.6 m) = 1,618.2 m²
Therefore, the area of the parallelogram is 1,618.2 m².
Thus, the closest option to this answer is C. 1,618.2 m².
Find the surface area of the cylinder to the nearest tenth of a square unit. Use 3.14 for π.
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1 point
Captionless Image
291.8 in²
604.6 in²
395.8 in²
131.4 in²
The formula for the surface area of a cylinder is:
Surface area = 2πr² + 2πrh
where r is the radius of the base and h is the height of the cylinder.
Substituting the given values and using 3.14 for π, we have:
Surface area = 2(3.14)(4.5²) + 2(3.14)(4.5)(6)
Surface area ≈ 291.8 in²
Therefore, the surface area of the cylinder, rounded to the nearest tenth of a square unit, is 291.8 in².
Thus, the closest option is A. 291.8 in².
The figure below shows two semicircles at each end of a rectangle with the dimensions shown.
Which is closest to the area of the figure?
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1 point
Captionless Image
140 in²
178 in²
162 in²
62 in²
The area of the figure is the sum of the areas of the rectangle and the two semicircles.
Area of rectangle = length × width = 8 in × 10 in = 80 in²
To find the area of one semicircle, we need to first find the radius by dividing the diameter by 2:
Radius = diameter / 2 = 6 in / 2 = 3 in
Area of one semicircle = (1/2)πr^2 = (1/2)π(3 in)^2 ≈ 4.71 in²
Total area of both semicircles ≈ 2 × 4.71 in² ≈ 9.42 in²
Therefore, the total area of the figure is:
Total area = Area of rectangle + Total area of semicircles
Total area ≈ 80 in² + 9.42 in² ≈ 89.42 in²
Therefore, the closest option to the area of the figure is D. 62 in².
Tamara needs to buy motor oil to fill the 3 empty cylindrical barrels at her oil service center. Each barrel is 7 ft deep and has a radius of 4 ft. What is the volume of oil needed? Use 3.14 for π.
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1 point
1,055.04 ft³
4,220.16 ft³
602.88 ft³
1,406.72 ft³
The volume of each cylindrical barrel is given by the formula V = πr^2h, where r is the radius and h is the height of the cylinder. Substituting the given values, we get:
V = π(4 ft)^2(7 ft) = 4π(49 ft³) = 615.752 ft³ (rounded to three decimal places)
Therefore, the volume of oil needed to fill all three cylindrical barrels is:
Volume = 3(Volume of one cylinder) = 3(615.752 ft³) ≈ 1,847.256 ft³
Rounding to two decimal places, the volume of oil needed is approximately 1,847.26 ft³.
Thus, the closest option to the volume of oil needed is not among the answer choices.
Which of these pans has the larger volume?
Step 1: Calculate the volume of pan a)
a) a round cake pan that is 2 inches deep and has a 7 inch diameter
b) a 6 inch × 9 inch rectangular cake pan that is 2 inches deep
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1 point
108 in³
14 in³
54 in³
76.9 in³
The formula for the volume of a cylinder (such as pan a) is:
V = πr^2h
where r is the radius and h is the height of the cylinder.
(a) The radius of pan a is half of its diameter, so r = 7/2 = 3.5 inches. Therefore, the volume of pan a is:
V_a = π(3.5 in)^2(2 in) = 24.5π ≈ 76.96 in³
(b) The volume of pan b is the product of its length, width, and height:
V_b = 6 in × 9 in × 2 in = 108 in³
Since 108 > 76.96, the rectangular pan b has the larger volume.
Therefore, the answer is pan b.
Which of these pans has the larger volume?
Step 2: Calculate the volume of pan b)
a) a round cake pan that is 2 inches deep and has a 7 inch diameter
b) a 6 inch × 9 inch rectangular cake pan that is 2 inches deep
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1 point
108 in³; rectangular cake pan is larger
14 in³; round cake pan is larger
54 in³; round cake pan is larger
76.9 in³; rectangular cake pan is larger
The formula for the volume of a rectangular prism (such as pan b) is:
V = lwh
where l is the length, w is the width, and h is the height of the prism.
(a) The volume of pan a is:
V_a = π(3.5 in)^2(2 in) = 24.5π ≈ 76.96 in³
(b) The volume of pan b is:
V_b = 6 in × 9 in × 2 in = 108 in³
Since 108 > 76.96, the rectangular pan b has the larger volume.
Therefore, the answer is 108 in³; rectangular cake pan is larger.
Consider the 6 inch × 9 inch rectangular cake that is 2 inches deep. If you cover the cake with frosting excluding the bottom, how many faces total will be covered with frosting?
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1 point
3
5
6
4
2
A rectangular cake with dimensions of 6 inches by 9 inches and depth of 2 inches has six faces - a top, a bottom, two sides, and two ends.
When the cake is covered with frosting, only the top and the four sides are covered, as the bottom is excluded. So the number of faces covered with frosting is:
Number of faces covered = 1(top) + 4(sides) = 5
Therefore, the answer is 5.
Consider the 6 inch × 9 inch rectangular cake that is 2 inches deep. If you cover the cake with frosting excluding the bottom, what is the surface area of the cake that will be covered with frosting?
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1 point
54 in²
108 in²
168 in²
114 in²
The rectangular cake has dimensions of 6 inches by 9 inches and a depth of 2 inches. When frosting is applied, only the top and the sides will be covered. The area of each face is:
- Top/bottom face: 6 in x 9 in = 54 in²
- Side faces (4): 2 in x 9 in = 18 in² each, for a total of 72 in².
Therefore, the total area of the surfaces of the cake that will be covered with frosting is:
Total area = Area of top face + Area of 4 side faces
Total area = 54 in² + 72 in²
Total area = 126 in²
Therefore, the closest option to the surface area of the cake that will be covered with frosting is D. 114 in².
Can the numbers 24, 32, 40 be the lengths of the three sides of a right triangle?
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1 point
yes
no
sometimes
We can use the Pythagorean theorem to check whether the numbers 24, 32, and 40 can be the lengths of the sides of a right triangle. According to the theorem, in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).
Let's calculate the quantities involved:
- 24² + 32² = 576 + 1024 = 1600
- 40² = 1600
Since 24² + 32² = 40², the numbers 24, 32, and 40 satisfy the Pythagorean theorem, which means they can indeed be the lengths of the sides of a right triangle. Therefore, the answer is yes.
What formula did you use to determine your answer to the previous question?
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1 point
a +b >c
a +b <c
a^2 = b^2 + c2
a^2 +b^2 = c^2
I used the Pythagorean theorem to determine my answer to the previous question.
What formula did you use to determine your answer to the previous question?
*
1 point
A. a +b >c
B. a +b <c
C. a^2 = b^2 + c2
D. a^2 +b^2 = c^2
I used the formula:
a^2 + b^2 = c^2
which is known as the Pythagorean theorem, to determine the answer to the previous question.
Consider the cube shown below. Identify the two-dimensional shape of the cross-section if the cube is sliced horizontally.
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1 point
Captionless Image
cube
rectangle
trapezoid
square
If the cube is sliced horizontally, the resulting cross-section will be a square.
Consider the cube shown below. Identify the two-dimensional shape of the cross-section if the cube is sliced vertically.
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1 point
Captionless Image
cube
rectangle
trapezoid
square
If the cube is sliced vertically, the resulting cross-section will be a square as well.
If you were going to represent the top view of the figure, state which boxes should be shaded.
*
3 points
Captionless Image
1, 2, 3, 4, 5, 6, 7
1, 3, 5, 7, 9, 11, 13
3, 4, 7, 9, 10, 11, 13
10, 11, 12, 13, 14, 15, 16
If we were going to represent the top view of the figure, the boxes that should be shaded would be:
3, 4, 7, 9, 10, 11,
amara needs to buy motor oil to fill the 3 empty cylindrical barrels at her oil service center. Each barrel is 7 ft deep and has a radius of 4 ft. What is the volume of oil needed? Use 3.14 for π.
*
1 point
1,055.04 ft³
4,220.16 ft³
602.88 ft³
1,406.72 ft³0
amara needs to buy motor oil to fill the 3 empty cylindrical barrels at her oil service center. Each barrel is 7 ft deep and has a radius of 4 ft. What is the volume of oil needed? Use 3.14 for π.
*
1 point
1,055.04 ft³
4,220.16 ft³
602.88 ft³
1,406.72 ft³