Use the image to answer the question.
An illustration shows a three dimensional composite figure formed by a rectangular prism with a missing section. The missing section is also in the shape of a rectangular prism. The top, right, and front faces of the figure are visible. "The faces and edges that are not visible are indicated by dashed lines. The rectangular prism has a length of 13.7 centimeters and a height of 11.5 centimeters. The missing section is removed from the bottom right corner of the rectangular prism. The missing section is a rectangular prism that shares a width of 3 centimeters with the rest of the figure. The missing rectangular prism section has a length of 7.5 centimeters and a height of 7.5 centimeters. The remaining length to the left of the missing section both measures 6.2 centimeters. The remaining height above the missing section measures 4 centimeters.
Solve for the total surface area of the figure.
To find the total surface area of the figure, we need to find the surface area of the rectangular prism and subtract the surface area of the missing section.
Surface area of the rectangular prism:
Total surface area = 2lw + 2lh + 2wh
= 2(13.7*11.5) + 2(13.7*4) + 2(11.5*4)
= 2(157.55) + 2(54.8) + 2(46)
= 315.1 + 109.6 + 92
= 516.7 cm^2
Surface area of the missing section:
Since the missing section is the same shape as the rectangular prism and only a part of it is missing, we can find the surface area by subtracting the surface area of the missing section from the surface area of the rectangular prism:
= 2(7.5*7.5) + 2(7.5*3) + 2(7.5*3)
= 2(56.25) + 2(22.5) + 2(22.5)
= 112.5 + 45 + 45
= 202.5 cm^2
Total surface area of the figure:
516.7 cm^2 - 202.5 cm^2
= 314.2 cm^2
Therefore, the total surface area of the figure is 314.2 cm^2.
Use the image to answer the question.
An illustration shows a three dimensional composite figure formed by a rectangular prism with a missing section. The missing section is in the shape of two rectangular prisms. With the section removed, the figure resembles three steps. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism has a length of 12 centimeters at the bottom, a width of 2 centimeters, and a height of 18 centimeters. The top length of the rectangular prism is divided equally across the three steps. Each step has a length of 4 centimeters. The right side height of the rectangular prism is divided equally along the three steps. Each step has a height of 6 centimeters.
What is the total surface area of the figure?
To find the total surface area of the figure, we need to find the surface area of the rectangular prism and subtract the surface area of the missing sections.
First, let's find the surface area of the rectangular prism:
Total surface area = 2lw + 2lh + 2wh
= 2(12*18) + 2(12*2) + 2(18*2)
= 2(216) + 2(24) + 2(36)
= 432 + 48 + 72
= 552 cm^2
Now, let's find the surface area of the missing sections. Since the missing section consists of two rectangular prisms, one with a length of 8 cm, a width of 2 cm, and a height of 12 cm, and the other with a length of 4 cm, a width of 2 cm, and a height of 6 cm, we can find their surface areas and then add them together.
Surface area of the first missing section = 2(8*12) + 2(8*2) + 2(12*2) = 192 + 32 + 48 = 272 cm^2
Surface area of the second missing section = 2(4*6) + 2(4*2) + 2(6*2) = 48 + 16 + 24 = 88 cm^2
Total surface area of the missing sections = 272 cm^2 + 88 cm^2 = 360 cm^2
Finally, to find the total surface area of the figure, we subtract the surface area of the missing sections from the surface area of the rectangular prism:
552 cm^2 - 360 cm^2 = 192 cm^2
Therefore, the total surface area of the figure is 192 cm^2.
Use the image to answer the question.
An illustration shows a small rectangular prism placed on top of a large rectangular prism, to form a 2-tiered step. The edges that are not visible are marked with dashed lines. The length of the large rectangular prism on the bottom is 17 inches and the height is 6.5 inches. The small rectangular prism placed on top along the back edge shows a width of 14 inches, which aligns with the width of the bottom rectangular prism. The total height of both rectangles is 13 inches overall. The length of the large rectangular prism that is not covered by the small rectangular prism is 8.5 inches.
Find the surface area of the two-tiered steps.
To find the total surface area of the two-tiered steps, we first need to calculate the individual surface areas of both the large rectangular prism and the small rectangular prism, and then sum them up.
1. Start with the large rectangular prism:
- Front and back faces: 17 inches (length) x 6.5 inches (height) = 110.5 sq. inches x 2 = 221 sq. inches
- Top and bottom faces: 17 inches (length) x 14 inches (width) = 238 sq. inches x 2 = 476 sq. inches
- Side faces: 6.5 inches (height) x 14 inches (width) = 91 sq. inches x 2 = 182 sq. inches
Total surface area of the large rectangular prism: 221 sq. inches + 476 sq. inches + 182 sq. inches = 879 sq. inches
2. Move on to the small rectangular prism:
- Front and back faces: 8.5 inches (length) x 6.5 inches (height) = 55.25 sq. inches x 2 = 110.5 sq. inches
- Top and bottom faces: 8.5 inches (length) x 14 inches (width) = 119 sq. inches x 2 = 238 sq. inches
- Side faces: 6.5 inches (height) x 14 inches (width) = 91 sq. inches x 2 = 182 sq. inches
Total surface area of the small rectangular prism: 110.5 sq. inches + 238 sq. inches + 182 sq. inches = 530.5 sq. inches
3. Finally, add up the surface areas of the large and small rectangular prisms:
Total surface area of the two-tiered steps: 879 sq. inches + 530.5 sq. inches = 1409.5 sq. inches
Therefore, the surface area of the two-tiered steps is 1409.5 square inches.
Use the image to answer the question.
A square prism with a vertical rectangular portion removed from the bottom middle. The side of the square prism is 10 feet. The height of the portion removed from the middle, from the base upward, is 5 feet. The width of the remaining two legs on the left and right of the removed portion is 4 feet each.
A giant model of a magnet is being built for a museum exhibit. What is the total surface area of the prop that will need to be painted if the depth of the magnet is 3 feet?
To find the total surface area of the prop that needs to be painted for the magnet model, we need to calculate the surface area of the entire square prism and then subtract the surface area of the rectangular portion removed.
First, let's calculate the total surface area of the square prism:
- The area of one side of the square prism (10 feet x 10 feet): 100 square feet
- There are 4 sides to the square prism, so the total area of the sides is: 4 x 100 = 400 square feet
- The area of the top and bottom faces of the square prism (10 feet x 10 feet): 100 square feet each
- There are 2 top and bottom faces, so the total area of the top and bottom faces is: 2 x 100 = 200 square feet
- The total surface area of the entire square prism is: 400 + 200 = 600 square feet
Next, let's calculate the surface area of the rectangular portion that was removed:
- The area of the front and back faces of the removed rectangular portion (4 feet x 5 feet): 20 square feet each
- There are 2 front and back faces, so the total area of the front and back faces is: 2 x 20 = 40 square feet
- The area of the top and bottom faces of the removed rectangular portion (4 feet x 10 feet): 40 square feet each
- There are 2 top and bottom faces, so the total area of the top and bottom faces is: 2 x 40 = 80 square feet
- The total surface area of the removed rectangular portion is: 40 + 80 = 120 square feet
Now, let's find the surface area of the prop that will need to be painted by subtracting the surface area of the removed portion from the surface area of the entire square prism:
600 square feet - 120 square feet = 480 square feet
Therefore, the total surface area of the prop that will need to be painted for the magnet model is 480 square feet.
A toy truck is comprised of a rectangular cab and a shipping container that it is carrying. What is the total surface area of the truck (excluding the wheels)?
(1 point)
To find the total surface area of the toy truck (excluding the wheels), we need to calculate the surface area of both the cab and the shipping container separately, and then add them together.
Let's start with the cab:
- The cab is in the shape of a rectangular prism.
- Let's say the dimensions of the cab are: length = L, width = W, height = H.
The surface area of the rectangular prism is calculated as:
Surface Area = 2lw + 2lh + 2wh
Surface Area of the cab = 2(L*W) + 2(L*H) + 2(W*H)
Next, let's move on to the shipping container:
- The shipping container is also a rectangular prism.
- Let's say the dimensions of the container are: length = Lc, width = Wc, height = Hc.
The surface area of the rectangular prism (shipping container) is calculated as:
Surface Area of the container = 2(Lc*Wc) + 2(Lc*Hc) + 2(Wc*Hc)
Now, to find the total surface area of the truck (excluding the wheels), we add the surface areas of the cab and the shipping container:
Total Surface Area of the truck = Surface Area of the cab + Surface Area of the container
You would need to know the specific dimensions of the cab and the shipping container (length, width, and height) to plug those values into the formulas above in order to calculate the total surface area of the toy truck.