The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. Since all the edge lengths are the same at 15.10 cm, l = 15.10 cm, w = 15.10 cm, and h = 15.10 cm. Substituting these values into the formula:
2(15.10 cm)(15.10 cm) + 2(15.10 cm)(15.10 cm) + 2(15.10 cm)(15.10 cm)
= (2)(15.10 cm)(15.10 cm + 15.10 cm + 15.10 cm)
= (2)(15.10 cm)(45.30 cm)
= (2)(681.30 cm^2)
= 1,362.60 cm^2
Therefore, the surface area of the right rectangular prism is C.1,368.06 cm^2.
What is the surface area of a right rectangular prism where each edge length measures 15.10 cm?
A.900 cm^2
B.1,350 cm^2
C.1,368.06 cm^2
D.8,208.36 cm^2
11 answers
Given that each square is 1 inch, find the surface area of this puzzle game.
A.54 cm^2
B.54 in.^2
C.18 in.^2
D.9 in.^2
A.54 cm^2
B.54 in.^2
C.18 in.^2
D.9 in.^2
To find the surface area of the puzzle game, we need to find the area of each side and sum them up.
Since each square is 1 inch, the length and width of each square on each face of the puzzle game would be 1 inch.
The puzzle game has 6 faces, so the total surface area is 6 * (1 inch * 1 inch) = 6 square inches.
Therefore, the surface area of the puzzle game is B. 54 in.^2
Since each square is 1 inch, the length and width of each square on each face of the puzzle game would be 1 inch.
The puzzle game has 6 faces, so the total surface area is 6 * (1 inch * 1 inch) = 6 square inches.
Therefore, the surface area of the puzzle game is B. 54 in.^2
A carry-on suitcase is 9.5 inches long, 16 inches wide, and 22.5 inches high. What is the surface area of the suitcase?
A.1,451.5 in.^2
B.725.75 in.^2
C.3,420 in.^2
D.96 in.^2
A.1,451.5 in.^2
B.725.75 in.^2
C.3,420 in.^2
D.96 in.^2
The surface area of the suitcase can be calculated by finding the area of each side and summing them up.
The front and back sides have dimensions of 9.5 inches (length) and 22.5 inches (height), so their combined area is 9.5 inches * 22.5 inches = 213.75 square inches.
The top and bottom sides have dimensions of 16 inches (width) and 22.5 inches (height), so their combined area is 16 inches * 22.5 inches = 360 square inches.
The left and right sides have dimensions of 9.5 inches (length) and 16 inches (width), so their combined area is 9.5 inches * 16 inches = 152 square inches.
Summing up the areas of all sides, we get 2 * 213.75 square inches + 2 * 360 square inches + 2 * 152 square inches = 427.5 square inches + 720 square inches + 304 square inches = 1,451.5 square inches.
Therefore, the surface area of the suitcase is A. 1,451.5 in.^2
The front and back sides have dimensions of 9.5 inches (length) and 22.5 inches (height), so their combined area is 9.5 inches * 22.5 inches = 213.75 square inches.
The top and bottom sides have dimensions of 16 inches (width) and 22.5 inches (height), so their combined area is 16 inches * 22.5 inches = 360 square inches.
The left and right sides have dimensions of 9.5 inches (length) and 16 inches (width), so their combined area is 9.5 inches * 16 inches = 152 square inches.
Summing up the areas of all sides, we get 2 * 213.75 square inches + 2 * 360 square inches + 2 * 152 square inches = 427.5 square inches + 720 square inches + 304 square inches = 1,451.5 square inches.
Therefore, the surface area of the suitcase is A. 1,451.5 in.^2
Lizzie and her wife need to paint the walls of their bedroom. The room is 12 feet by 14 feet, and it has a ceiling that is 10 feet high. What is the area that they need to paint?
___ft.2
___ft.2
To find the area that Lizzie and her wife need to paint, we need to calculate the area of the four walls and the ceiling.
The area of the four walls can be found by multiplying the perimeter of the room by the height of the room.
The perimeter of the room is 2 * (length + width) = 2 * (12 feet + 14 feet) = 2 * 26 feet = 52 feet.
The area of the four walls is then 52 feet * 10 feet = 520 square feet.
The area of the ceiling can be found by multiplying the length and width of the room.
The area of the ceiling is 12 feet * 14 feet = 168 square feet.
Therefore, Lizzie and her wife need to paint an area of 520 square feet + 168 square feet = 688 square feet.
The area of the four walls can be found by multiplying the perimeter of the room by the height of the room.
The perimeter of the room is 2 * (length + width) = 2 * (12 feet + 14 feet) = 2 * 26 feet = 52 feet.
The area of the four walls is then 52 feet * 10 feet = 520 square feet.
The area of the ceiling can be found by multiplying the length and width of the room.
The area of the ceiling is 12 feet * 14 feet = 168 square feet.
Therefore, Lizzie and her wife need to paint an area of 520 square feet + 168 square feet = 688 square feet.
Find the surface area of a rectangular pyramid with these measurements: l = 15 m, w = 12 m, and h = 10 m. Express your answer as a decimal rounded to the nearest hundredth.
___m^2
___m^2
To find the surface area of a rectangular pyramid, we need to calculate the area of each of its faces and add them together.
The base of the pyramid is a rectangle with length l = 15 m and width w = 12 m.
The area of the base is l * w = 15 m * 12 m = 180 m^2.
The pyramid also has four triangular faces. The area of a triangle can be calculated using the formula (1/2) * base * height.
For the first triangular face, the base is the length l = 15 m and the height is the height of the pyramid h = 10 m.
The area of the first triangular face is (1/2) * 15 m * 10 m = 75 m^2.
For the second and third triangular faces, the base is the width w = 12 m and the height is the height of the pyramid h = 10 m.
The area of the second and third triangular faces together is 2 * (1/2) * 12 m * 10 m = 120 m^2.
For the fourth triangular face, the base is the diagonal of the base rectangle and the height is the height of the pyramid h = 10 m. We can use the Pythagorean theorem to find the diagonal.
The diagonal squared is equal to the sum of the squares of the length and width: diagonal^2 = l^2 + w^2.
diagonal^2 = 15 m^2 + 12 m^2 = 27 m^2.
Taking the square root of both sides gives: diagonal = sqrt(27) = 3 * sqrt(3) m.
The area of the fourth triangular face is (1/2) * diagonal * height = (1/2) * 3 * sqrt(3) m * 10 m = 15 sqrt(3) m^2.
Adding up all the areas, the total surface area of the rectangular pyramid is:
180 m^2 + 75 m^2 + 120 m^2 + 15 sqrt(3) m^2.
Now, rounding to the nearest hundredth:
180 + 75 + 120 ≈ 375
15 * 1.732 ≈ 25.98
So, the surface area of the rectangular pyramid is approximately 375 m^2 + 25.98 m^2 = 400.98 m^2.
Therefore, the surface area of the rectangular pyramid is approximately 400.98 m^2.
The base of the pyramid is a rectangle with length l = 15 m and width w = 12 m.
The area of the base is l * w = 15 m * 12 m = 180 m^2.
The pyramid also has four triangular faces. The area of a triangle can be calculated using the formula (1/2) * base * height.
For the first triangular face, the base is the length l = 15 m and the height is the height of the pyramid h = 10 m.
The area of the first triangular face is (1/2) * 15 m * 10 m = 75 m^2.
For the second and third triangular faces, the base is the width w = 12 m and the height is the height of the pyramid h = 10 m.
The area of the second and third triangular faces together is 2 * (1/2) * 12 m * 10 m = 120 m^2.
For the fourth triangular face, the base is the diagonal of the base rectangle and the height is the height of the pyramid h = 10 m. We can use the Pythagorean theorem to find the diagonal.
The diagonal squared is equal to the sum of the squares of the length and width: diagonal^2 = l^2 + w^2.
diagonal^2 = 15 m^2 + 12 m^2 = 27 m^2.
Taking the square root of both sides gives: diagonal = sqrt(27) = 3 * sqrt(3) m.
The area of the fourth triangular face is (1/2) * diagonal * height = (1/2) * 3 * sqrt(3) m * 10 m = 15 sqrt(3) m^2.
Adding up all the areas, the total surface area of the rectangular pyramid is:
180 m^2 + 75 m^2 + 120 m^2 + 15 sqrt(3) m^2.
Now, rounding to the nearest hundredth:
180 + 75 + 120 ≈ 375
15 * 1.732 ≈ 25.98
So, the surface area of the rectangular pyramid is approximately 375 m^2 + 25.98 m^2 = 400.98 m^2.
Therefore, the surface area of the rectangular pyramid is approximately 400.98 m^2.
What is the surface area of a square pyramid where the base edge is 1.5 cm and the slant height is 4 cm? Round your answer to the nearest hundredth.
___cm^2
___cm^2
The surface area of a square pyramid can be found by calculating the area of the base and the area of each of the four triangular faces and summing them.
The area of the base is equal to the square of the length of one side. In this case, the base edge is 1.5 cm, so the area of the base is (1.5 cm)^2 = 2.25 cm^2.
The area of each triangular face can be calculated using the formula (1/2) * base * height, where the base is the base edge of the pyramid and the height is the slant height. In this case, the base edge is 1.5 cm and the slant height is 4 cm.
The area of each triangular face is (1/2) * 1.5 cm * 4 cm = 6 cm^2.
Since the square pyramid has four triangular faces, the total area of the triangular faces is 4 * 6 cm^2 = 24 cm^2.
Adding the area of the base and the area of the triangular faces gives us the total surface area of the square pyramid:
2.25 cm^2 + 24 cm^2 = 26.25 cm^2.
Rounding to the nearest hundredth, the surface area of the square pyramid is approximately 26.25 cm^2.
Therefore, the surface area of the square pyramid is approximately 26.25 cm^2.
The area of the base is equal to the square of the length of one side. In this case, the base edge is 1.5 cm, so the area of the base is (1.5 cm)^2 = 2.25 cm^2.
The area of each triangular face can be calculated using the formula (1/2) * base * height, where the base is the base edge of the pyramid and the height is the slant height. In this case, the base edge is 1.5 cm and the slant height is 4 cm.
The area of each triangular face is (1/2) * 1.5 cm * 4 cm = 6 cm^2.
Since the square pyramid has four triangular faces, the total area of the triangular faces is 4 * 6 cm^2 = 24 cm^2.
Adding the area of the base and the area of the triangular faces gives us the total surface area of the square pyramid:
2.25 cm^2 + 24 cm^2 = 26.25 cm^2.
Rounding to the nearest hundredth, the surface area of the square pyramid is approximately 26.25 cm^2.
Therefore, the surface area of the square pyramid is approximately 26.25 cm^2.
1 answer