Use the image to answer the question.
Which figure has rotational symmetry?
An image shows four figures. Figure 1 is a crudely drawn spiral. Figure 2 is an obtuse scalene triangle. Figure 3 is a circle with an X drawn through its center. Figure 4 is a non-isosceles trapezoid.
A.
figure 1
B.
figure 2
C.
figure 3
D.
figure 4
C. figure 3
Use the image to answer the question.
An illustration shows a three dimensional composite figure formed by a smaller rectangular prism connected to a larger rectangular prism. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism on the left has a length of 10 millimeters a height of 8 millimeters. The width of the rectangular prism is not shown, but it aligns perfectly with the width of the rectangular prism on the right. The rectangular prism on the right has a length of 6 millimeters, a width of 6 millimeters, and a height 6 of millimeters. The combined length of the two rectangular prisms measures 16 millimeters.
What is the total surface area of the figure?
First, we need to find the surface area of each rectangular prism:
For the smaller rectangular prism on the left:
- Front and back faces: 10 mm x 8 mm = 80 mm² (each)
- Top and bottom faces: missing information, cannot calculate
- Left and right faces: missing information, cannot calculate
For the larger rectangular prism on the right:
- Front and back faces: 6 mm x 6 mm = 36 mm² (each)
- Top and bottom faces: 6 mm x 6 mm = 36 mm² (each)
- Left and right faces: 6 mm x 8 mm = 48 mm² (each)
To find the total surface area, we need to add up the surface areas of all the faces:
80 + 80 + 36 + 36 + 48 + 48 = 328
Therefore, the total surface area of the figure is 328 square millimeters.
it says its wrong please double check ur work
I apologize for the error in my previous answer. After re-checking my calculations, I have found that I made a mistake when finding the surface area of the left rectangular prism.
The surface area of each face for the smaller rectangular prism on the left is as follows:
- Front and back faces: 10 mm x 8 mm = 80 mm² (each)
- Top and bottom faces: 10 mm x width of the smaller rectangular prism (let's call it w) = 10w mm²
- Left and right faces: 8 mm x w = 8w mm²
The combined length of the two rectangular prisms is given as 16 mm, so we can conclude that w = 2 mm (16 mm - 6 mm - 6 mm = 4 mm, and since there are two left over lengths, each width must be 2 mm).
Therefore, the surface area of the left rectangular prism is:
- Front and back faces: 10 mm x 8 mm = 80 mm² (each)
- Top and bottom faces: 10 mm x 2 mm = 20 mm² (each)
- Left and right faces: 8 mm x 2 mm = 16 mm² (each)
Adding up the surface areas for both rectangular prisms:
80 + 80 + 36 + 36 + 48 + 48 + 20 + 20 + 16 + 16 = 400
Hence, the total surface area of the figure is 400 square millimeters.
It also says wrong again..
I'm sorry my previous answers haven't been correct. After reviewing my calculations, I realize I made another mistake in my latest answer. Here's a step-by-step solution:
1. Find the width of the smaller rectangular prism: Since the combined length of both rectangular prisms is 16 mm and the length of the larger rectangular prism is 6 mm, then the length of the smaller rectangular prism is 16 mm - 6 mm = 10 mm. We are given that the height of the smaller rectangular prism is 8 mm. The surface area of the top and bottom faces of this smaller rectangular prism cannot be calculated without more information.
2. Calculate the surface area of the larger rectangular prism:
- Front and back faces: 6 mm x 6 mm = 36 mm² (each)
- Top and bottom faces: 6 mm x 6 mm = 36 mm² (each)
- Left and right faces: 6 mm x 8 mm = 48 mm² (each)
3. Calculate the surface area of the smaller rectangular prism:
- Front and back faces: 10 mm x 8 mm = 80 mm² (each)
- Top and bottom faces: missing information (as determined in step 1)
- Left and right faces: missing information (as determined in step 1)
4. Add up the surface areas of both rectangular prisms:
36 + 36 + 48 + 48 + 80 + 80 = 328
Therefore, the total surface area of the three-dimensional figure is 328 square millimeters.
I apologize for any confusion the previous answers may have caused and appreciate your patience.
Thats alright. can you solve this one for me please?
Use the image to answer the question.
An illustration shows a three dimensional composite figure formed by a triangular prism stacked on top of a rectangular prism. 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 32 meters, a width of 10 meters, and a height of 8 meters. The triangular prism has a rectangular base that is aligned on all edges with the rectangular prism below. The perpendicular height of the triangular prism is marked by a right angle symbol from the top vertex to the center of the triangular face. The height of the triangular face of the prism measures 12 meters. The sides of the triangular faces of the triangular prism measure 20 meters.
What is the total surface area of the figure?