What is the order of the numbers from least to greatest?
A = 4.6 x 10–4 B = 2.4 x 10–3 C = 3.5 x 105 D = 6.3 x 10–4
A. C < A < B < D
B. D < A < C < B
C. B < C < A < D
D. A < D < B < C
A. C < A < B < D
Use the image to answer the question.
An illustration shows a pyramid with a rectangular base. The length of the base is labeled 14 centimeters and the width as 12 centimeters. The perpendicular heights from the apex to the base length of 14 is 10 centimeters and to the base width of 12 is 10.6 centimeters. The perpendicular heights are denoted by two right angle symbols on two of the lateral faces from the apex to the base by dashed lines.
What is the surface area of the rectangular pyramid?
(1 point)
cm2
We need to find the area of each face of the pyramid and add them together to get the total surface area.
First, let's find the area of the rectangular base:
Area = length x width = 14 cm x 12 cm = 168 cm^2
Now, let's find the area of each triangular face:
Area of face 1 = (1/2) x base x height = (1/2) x 14 cm x 10.6 cm = 74.2 cm^2
Area of face 2 = (1/2) x base x height = (1/2) x 12 cm x 10 cm = 60 cm^2
Area of face 3 = (1/2) x base x height = (1/2) x 14 cm x 10 cm = 70 cm^2
Area of face 4 = (1/2) x base x height = (1/2) x 12 cm x 10.6 cm = 63.6 cm^2
Now we can add up all the areas to get the total surface area:
168 cm^2 + 74.2 cm^2 + 60 cm^2 + 70 cm^2 + 63.6 cm^2 = 435.8 cm^2
Therefore, the surface area of the rectangular pyramid is 435.8 cm^2.
Use the image to answer the question.
An illustration shows a three dimensional composite figure formed by a right triangular prism placed 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 12 feet and a height of 8 feet. The width of the rectangular prism is not shown. The edges of the hidden side face of the right triangular prism align perfectly with the edges of the hidden top face of the rectangular prism. The right triangular prism is aligned to the left of the rectangular prism. The height of the right triangular prism is not shown. The total height of the left side of the figure is 20 feet. The right triangular prism has a width of 8 feet. The hypotenuse side of the right triangular prism has a length of 15 feet.
What is the surface area of the figure?
(1 point)
__ ft.2
We need to find the surface area of all the faces of the composite figure and add them together.
First, let's find the missing width of the rectangular prism. We know that the hypotenuse of the right triangular face is 15 feet, so we can use the Pythagorean theorem to find the missing side:
a^2 + b^2 = c^2
a^2 + 8^2 = 15^2
a^2 = 15^2 - 8^2
a^2 = 169
a = 13
So the missing width of the rectangular prism is 13 feet.
Now we can find the surface area of each face:
- Top face of rectangular prism: 12 ft x 13 ft = 156 ft^2
- Front face of rectangular prism: 8 ft x 13 ft = 104 ft^2
- Right face of rectangular prism: 8 ft x 20 ft = 160 ft^2
- Front face of right triangular prism: (1/2) x 8 ft x 15 ft = 60 ft^2
- Left face of right triangular prism: (1/2) x 8 ft x 20 ft = 80 ft^2
- Bottom face of right triangular prism: (1/2) x 13 ft x 15 ft = 97.5 ft^2
Note that the back face of the rectangular prism and the top face of the right triangular prism are not visible, so we don't need to include them in our calculation.
Now we can add up all the areas to get the total surface area:
156 ft^2 + 104 ft^2 + 160 ft^2 + 60 ft^2 + 80 ft^2 + 97.5 ft^2 = 657.5 ft^2
Therefore, the surface area of the composite figure is 657.5 ft^2.
Use the image to answer the question.
An illustration shows a 3-dimensional vertical rectangular prism that appears as the letter upper C, with a rectangular portion removed from the right center. The rectangular prism is 15 feet high, 10 feet wide, and 1 foot deep. The width of the portion removed from the middle on the right side is 7 feet across. The height of the remaining two arms left at the top and bottom is 4 feet each.
In Los Cabos, Mexico, there is a big sculpture of block letters that welcomes you. The image shows the letter C. What is its surface area?
(1 point)
_____ ft.2
We need to find the surface area of all the faces of the rectangular prism and subtract the surface area of the rectangular portion removed from the right center.
First, let's find the surface area of the rectangular prism:
- Front and back faces: 15 ft x 10 ft = 150 ft^2 (there are two of these)
- Top and bottom faces: 10 ft x 1 ft = 10 ft^2 (there are two of these)
- Left face: 15 ft x 1 ft = 15 ft^2
- Right face: 15 ft x 1 ft = 15 ft^2
Total surface area of rectangular prism = 2(150 ft^2) + 2(10 ft^2) + 15 ft^2 + 15 ft^2 = 350 ft^2
Now let's find the surface area of the rectangular portion removed from the right center:
- Front and back faces: 15 ft x 1 ft = 15 ft^2 (there are two of these)
- Top and bottom faces: 4 ft x 7 ft = 28 ft^2 (there are two of these)
- Left face: 15 ft x 4 ft = 60 ft^2
- Right face: This face has been removed and does not contribute to the surface area.
Total surface area of removed portion = 2(15 ft^2) + 2(28 ft^2) + 60 ft^2 = 146 ft^2
Now we can subtract the surface area of the removed portion from the surface area of the rectangular prism:
350 ft^2 - 146 ft^2 = 204 ft^2
Therefore, the surface area of the letter C is 204 ft^2.
Use the image to answer the question.
An illustration shows a triangular prism. The front triangular face is visible. The right rectangular face is visible. The visible rectangular face has a width of 5 centimeters and length of 11 centimeters. The sides and edges that are not visible are indicated by dashed lines. The legs of the triangular face are labeled 3 centimeters and 4 centimeters. The hypotenuse shares the same label as the width of the visible rectangular face.
What is the surface area of the triangular prism?
(1 point)
_____ square centimeters
First, let's find the height of the triangular face using the Pythagorean theorem:
a^2 + b^2 = c^2
3^2 + 4^2 = c^2
9 + 16 = c^2
25 = c^2
c = 5
So the height of the triangular face is 5 centimeters.
Now we can find the surface area of each face:
- Front and back triangular faces: (1/2) x 3 cm x 4 cm = 6 cm^2 (there are two of these)
- Top rectangular face: 3 cm x 5 cm = 15 cm^2
- Bottom rectangular face: 3 cm x 5 cm = 15 cm^2
- Left rectangular face: 4 cm x 5 cm = 20 cm^2
- Right rectangular face: 4 cm x 11 cm = 44 cm^2
Note that we don't count the area of the diagonally oriented rectangular faces since they are not visible in the illustration.
Now we can add up all the areas to get the total surface area:
2(6 cm^2) + 15 cm^2 + 15 cm^2 + 20 cm^2 + 44 cm^2 = 106 cm^2
Therefore, the surface area of the triangular prism is 106 square centimeters.
Use the image to answer the question.
An illustration shows a rectangular prism with its length measuring 17 centimeters, width measuring 10 centimeters, and height measuring 4 centimeters. The edges that are not visible are marked as dashed lines.
Jerry wants to wrap a present in a box for his mother. The box measures 10 cm wide, 4 cm high, and 17 cm long. How much wrapping paper will Jerry need to wrap the present?
(1 point)
surface area = ___ cm2