Use the image to answer the question.
An illustration shows a rectangular prism with length 10 inches, width 9 inches, and height 3 inches. The top, front, and right faces are visible. The edges that are not visible are represented by dashed lines.
What is the surface area of the rectangular prism?
To find the surface area of a rectangular prism, we need to find the area of each of the six faces and then add them together.
The top and bottom faces are both rectangles with dimensions 10 inches by 9 inches. So, each top and bottom face has an area of 10 inches x 9 inches = 90 square inches. Since there are two of these faces, the total area of the top and bottom faces is 90 square inches x 2 = 180 square inches.
The front and back faces are also rectangles with dimensions 10 inches by 3 inches. So, each front and back face has an area of 10 inches x 3 inches = 30 square inches. Since there are two of these faces, the total area of the front and back faces is 30 square inches x 2 = 60 square inches.
The right and left faces are rectangles with dimensions 9 inches by 3 inches. So, each right and left face has an area of 9 inches x 3 inches = 27 square inches. Since there are two of these faces, the total area of the right and left faces is 27 square inches x 2 = 54 square inches.
Therefore, the total surface area of the rectangular prism is 180 square inches (top and bottom) + 60 square inches (front and back) + 54 square inches (right and left) = 294 square inches.
Therefore, the surface area of the rectangular prism is 294 square inches.
What is the missing width of a rectangular prism with a length of 6 cm, a height of 4 cm, and a surface area of 188 cm2 ?
To find the missing width of the rectangular prism, we first need to calculate the surface area using the given dimensions and then solve for the missing width.
The formula for the surface area of a rectangular prism is:
Surface Area = 2lw + 2lh + 2wh
Where:
l = length
h = height
w = width
Given:
l = 6 cm
h = 4 cm
Surface Area = 188 cm^2
Substitute the given values into the formula:
188 = 2(6)(w) + 2(6)(4) + 2(w)(4)
188 = 12w + 48 + 8w
188 = 20w + 48
20w = 140
w = 140 / 20
w = 7
Therefore, the missing width of the rectangular prism is 7 cm.
What does surface area measure?(1 point)
Responses
capacity
capacity
volume
volume
the outside of a three-dimensional shape
the outside of a three-dimensional shape
the inside of a three-dimensional shape
the outside of a three-dimensional shape
How many two-dimensional shapes make up a rectangular prism? (1 point)
Responses
three
three
four
four
eight
eight
six
six
Use the image to answer the question.
An illustration shows a rectangular prism with length 12 inches, width 5 inches, and height 3 inches. The top, front, and right faces are visible. The edges that are not visible are represented by dashed lines.
Solve for the surface area of the rectangular prism.
(1 point)
Responses
111 square inches
111 square inches
270 square inches
270 square inches
180 square inches
180 square inches
222 square inches
To find the surface area of a rectangular prism, we first need to calculate the area of each of the six faces and then sum them up.
Given:
Length = 12 inches
Width = 5 inches
Height = 3 inches
Calculate the area of each face:
1. Top and bottom faces: 2 * (Length * Width) = 2 * (12 * 5) = 2 * 60 = 120 square inches
2. Front and back faces: 2 * (Length * Height) = 2 * (12 * 3) = 2 * 36 = 72 square inches
3. Right and left faces: 2 * (Width * Height) = 2 * (5 * 3) = 2 * 15 = 30 square inches
Now, add up the areas of all six faces:
120 (top and bottom) + 72 (front and back) + 30 (right and left) = 222 square inches
Therefore, the surface area of the rectangular prism is 222 square inches.
So, the correct response is:
222 square inches
Use the image to answer the question.
An illustration shows a cube with side 1.5 meters. The top, front, and right faces are visible. The edges that are not visible are represented by dashed lines.
What is the surface area of the cube?
(1 point)
Responses
13.5 square meters
13.5 square meters
27 square meters
27 square meters
4.5 square meters
4.5 square meters
18 square meters