The surface area of a Rubik's Cube can be found by calculating the area of each face and then adding them up. Since a Rubik's Cube has 6 faces, each measuring 1 inch by 1 inch, the total surface area is:
6 * (1 inch * 1 inch) = 6 square inches
Therefore, the correct answer is:
O 6in^2
Given that each square is 1 inch, find the surface area of a Rubrics cube.
(1 point)
O 18in .^ 2
O 54c * m ^ 2
O 9in .^ 2
O 54in .^ 2
13 answers
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? (1 point)
O 96in .^ 2
1, 451.5in .^ 2
O 3, 420in .^ 2
O 725.75i * n ^ 2
O 96in .^ 2
1, 451.5in .^ 2
O 3, 420in .^ 2
O 725.75i * n ^ 2
The surface area of a rectangular prism (like a suitcase) can be found by adding up the areas of all six faces.
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.
Plugging in the given values, we have:
2(9.5 inches * 16 inches) + 2(9.5 inches * 22.5 inches) + 2(16 inches * 22.5 inches)
= 2(152 square inches) + 2(213.75 square inches) + 2(360 square inches)
= 304 square inches + 427.5 square inches + 720 square inches
= 1451.5 square inches
Therefore, the surface area of the suitcase is:
O 1451.5in^2
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.
Plugging in the given values, we have:
2(9.5 inches * 16 inches) + 2(9.5 inches * 22.5 inches) + 2(16 inches * 22.5 inches)
= 2(152 square inches) + 2(213.75 square inches) + 2(360 square inches)
= 304 square inches + 427.5 square inches + 720 square inches
= 1451.5 square inches
Therefore, the surface area of the suitcase is:
O 1451.5in^2
Find the surface area of a rectangular pyramid with these measurements: l = 15m w = 12m , and h = 10m Express your answer as a decimal rounded to the nearest hundredth. (1 point)
The formula for the surface area of a rectangular pyramid is given by:
Surface area = l * w + l * sqrt((w/2)^2 + h^2) + w * sqrt((l/2)^2 + h^2)
Plugging in the given values, we have:
Surface area = 15m * 12m + 15m * sqrt((12m/2)^2 + 10m^2) + 12m * sqrt((15m/2)^2 + 10m^2)
Surface area = 180m^2 + 15m * sqrt((6m)^2 + 100m^2) + 12m * sqrt((7.5m)^2 + 100m^2)
Surface area ≈ 180m^2 + 15m * sqrt(36m^2 + 100m^2) + 12m * sqrt(56.25m^2 + 100m^2)
Surface area ≈ 180m^2 + 15m * sqrt(136m^2) + 12m * sqrt(156.25m^2)
Surface area ≈ 180m^2 + 15m * 11.66m + 12m * 12.5m
Surface area ≈ 180m^2 + 174.9m^2 + 150m^2
Surface area ≈ 504.9m^2
Therefore, the surface area of the rectangular pyramid is approximately:
504.9m^2
Surface area = l * w + l * sqrt((w/2)^2 + h^2) + w * sqrt((l/2)^2 + h^2)
Plugging in the given values, we have:
Surface area = 15m * 12m + 15m * sqrt((12m/2)^2 + 10m^2) + 12m * sqrt((15m/2)^2 + 10m^2)
Surface area = 180m^2 + 15m * sqrt((6m)^2 + 100m^2) + 12m * sqrt((7.5m)^2 + 100m^2)
Surface area ≈ 180m^2 + 15m * sqrt(36m^2 + 100m^2) + 12m * sqrt(56.25m^2 + 100m^2)
Surface area ≈ 180m^2 + 15m * sqrt(136m^2) + 12m * sqrt(156.25m^2)
Surface area ≈ 180m^2 + 15m * 11.66m + 12m * 12.5m
Surface area ≈ 180m^2 + 174.9m^2 + 150m^2
Surface area ≈ 504.9m^2
Therefore, the surface area of the rectangular pyramid is approximately:
504.9m^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. (1 point)
To find the surface area of a square pyramid, we need to calculate the area of the base and the area of the four triangular faces, and then sum them up.
The formula for the surface area of a square pyramid is given by:
Surface area = base area + 4 * (0.5 * base edge * slant height)
The base area of a square pyramid is simply the area of a square, given by:
Base area = base edge^2
Plugging in the given values, we have:
Base area = (1.5 cm)^2 = 2.25 cm^2
And the formula for the surface area becomes:
Surface area = 2.25 cm^2 + 4 * (0.5 * 1.5 cm * 4 cm)
Surface area = 2.25 cm^2 + 4 * (0.5 * 6 cm^2)
Surface area = 2.25 cm^2 + 4 * 3 cm^2
Surface area = 2.25 cm^2 + 12 cm^2
Surface area = 14.25 cm^2
Rounded to the nearest hundredth, the surface area of the square pyramid is approximately:
14.25 cm^2
The formula for the surface area of a square pyramid is given by:
Surface area = base area + 4 * (0.5 * base edge * slant height)
The base area of a square pyramid is simply the area of a square, given by:
Base area = base edge^2
Plugging in the given values, we have:
Base area = (1.5 cm)^2 = 2.25 cm^2
And the formula for the surface area becomes:
Surface area = 2.25 cm^2 + 4 * (0.5 * 1.5 cm * 4 cm)
Surface area = 2.25 cm^2 + 4 * (0.5 * 6 cm^2)
Surface area = 2.25 cm^2 + 4 * 3 cm^2
Surface area = 2.25 cm^2 + 12 cm^2
Surface area = 14.25 cm^2
Rounded to the nearest hundredth, the surface area of the square pyramid is approximately:
14.25 cm^2
Niko has an outdoor play tent in the form of a regular triangular pyramid, covered in fabric on all four sides. The surface area of the tent is 100ft .^ 2 , the base is 6 ft., and the slant height is 8 ft. What is the height of the base to the nearest tenth? (1 point)
O 372 ft.
O 57.3 ft.
O 9.3 ft.
O 6.5 ft.
O 372 ft.
O 57.3 ft.
O 9.3 ft.
O 6.5 ft.
To find the height of the base of the triangular pyramid, we need to use the formula for surface area and solve for the height.
The formula for the surface area of a triangular pyramid is given by:
Surface area = (1/2) * base perimeter * slant height + base area
Since the pyramid has a regular triangular base, the base area is given by:
Base area = (sqrt(3)/4) * base edge^2
Plugging in the given values, we have:
100ft^2 = (1/2) * (3 * 6ft) * 8ft + (sqrt(3)/4) * (6ft)^2
100ft^2 = 9ft * 8ft + (sqrt(3)/4) * 36ft^2
100ft^2 = 72ft^2 + (sqrt(3)/4) * 36ft^2
100ft^2 = 72ft^2 + (sqrt(3)/4) * 1296ft^2
100ft^2 = 72ft^2 + 324sqrt(3)ft^2
28ft^2 = 324sqrt(3)ft^2
sqrt(3)ft^2 = 28ft^2 / 324ft^2
sqrt(3)ft^2 ≈ 0.0864ft^2
Height of base = sqrt(3) * base edge
Height of base = sqrt(3) * 6ft
Height of base ≈ 6 * sqrt(3) ft
Height of base ≈ 10.39 ft
Therefore, the height of the base of the triangular pyramid is approximately:
O 10.4 ft
The formula for the surface area of a triangular pyramid is given by:
Surface area = (1/2) * base perimeter * slant height + base area
Since the pyramid has a regular triangular base, the base area is given by:
Base area = (sqrt(3)/4) * base edge^2
Plugging in the given values, we have:
100ft^2 = (1/2) * (3 * 6ft) * 8ft + (sqrt(3)/4) * (6ft)^2
100ft^2 = 9ft * 8ft + (sqrt(3)/4) * 36ft^2
100ft^2 = 72ft^2 + (sqrt(3)/4) * 36ft^2
100ft^2 = 72ft^2 + (sqrt(3)/4) * 1296ft^2
100ft^2 = 72ft^2 + 324sqrt(3)ft^2
28ft^2 = 324sqrt(3)ft^2
sqrt(3)ft^2 = 28ft^2 / 324ft^2
sqrt(3)ft^2 ≈ 0.0864ft^2
Height of base = sqrt(3) * base edge
Height of base = sqrt(3) * 6ft
Height of base ≈ 6 * sqrt(3) ft
Height of base ≈ 10.39 ft
Therefore, the height of the base of the triangular pyramid is approximately:
O 10.4 ft
You have to pick one of the options given
Apologies for the mistake. Based on the given options, the closest height of the base to the nearest tenth would be:
O 9.3 ft.
O 9.3 ft.
A gift box is being constructed in the shape of a right rectangular prism. The base is 15 inches squared and the height is 5 inches. What will the volume of the gift box be? (1 point)
4
4
The volume of a right rectangular prism is given by the formula:
Volume = length * width * height
In this case, the base is 15 square inches (which is equal to the length multiplied by the width). The height is given as 5 inches. Therefore, the volume of the gift box can be found as:
Volume = 15 inches^2 * 5 inches
Volume = 75 inches^3
Therefore, the volume of the gift box will be:
75 inches^3
Volume = length * width * height
In this case, the base is 15 square inches (which is equal to the length multiplied by the width). The height is given as 5 inches. Therefore, the volume of the gift box can be found as:
Volume = 15 inches^2 * 5 inches
Volume = 75 inches^3
Therefore, the volume of the gift box will be:
75 inches^3
1 answer