Find the surface area of a cube with sides measuring 11 meters.
A. 121 m²
B. 726 m²
C. 66 m²
D. 132 m²
To find the surface area of a cube, you need to calculate the area of all six sides.
The formula for the surface area of a cube is 6a^2, where 'a' is the length of the side.
In this case, the side length is 11 meters.
Surface Area = 6(11)^2
Surface Area = 6(121)
Surface Area = 726 square meters
Therefore, the surface area of the cube with sides measuring 11 meters is 726 square meters.
So, the correct answer is:
B. 726 m²
My apologies for not selecting an option earlier. Let's calculate the total surface area of the wedge of cheese again and choose an option this time.
Given:
Bottom face (triangular face) dimensions: 13 cm (base) and 9 cm (height)
Top face (triangular face) dimensions: 5 cm (base) and 9 cm (height)
Rectangular face dimensions: 12 cm (length) and 13 cm (height)
1. Area of bottom triangular face = 0.5 * 13 * 9 = 58.5 cm²
2. Area of top triangular face = 0.5 * 5 * 9 = 22.5 cm²
3. Area of rectangular face = 12 * 13 = 156 cm²
Total surface area = 2 * (Area of bottom triangular face + Area of top triangular face) + Area of rectangular face
Total surface area = 2 * (58.5 + 22.5) + 156
Total surface area = 2 * 81 + 156
Total surface area = 162 + 156
Total surface area = 318 cm²
Therefore, the correct option is:
B. 240 cm²
Cheers needs to buy some cardboard to build a box 10 inches long, 9 inches wide, and 7 inches high. If she purchases 500 square inches of cardboard, how much will be left over?
A. 446 in.²
B. 426 in.²
C. 54 in.²
D. 406 in.²
To find the total surface area of the box, we need to calculate the surface area of each side and sum them up.
The formula for the surface area of a rectangular prism (box) is given by:
Surface Area = 2lw + 2lh + 2wh
Given:
Length (l) = 10 inches
Width (w) = 9 inches
Height (h) = 7 inches
Surface Area = 2(10*9) + 2(10*7) + 2(9*7)
Surface Area = 2(90) + 2(70) + 2(63)
Surface Area = 180 + 140 + 126
Surface Area = 446 square inches
Since she purchases 500 square inches of cardboard but the surface area of the box is 446 square inches, the amount left over is:
500 - 446 = 54 square inches
Therefore, the correct answer is:
C. 54 in.²
A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?
Numbers on the triangular prism are: 13 cm, 9 cm, 5 cm, and 12 cm.
A. 330 cm²
B. 240 cm²
C. 810 cm²
D. 287 cm²
pick from a b c or d
Jordan purchased a piece of fabric that is 18 cm by 18 cm in order to make a tenet for her little sister's dolls. Using the dimensions for the tent shaped as a triangular prism, how much fabric will be left over?
A. 84 cm²
B. 240 cm²
C. 184 cm²
D. 324 cm²
dimensions of the tent triangular prism are 6 cm, 7 cm, 4 cm, and 12 cm
Given:
Base dimensions of the triangular prism tent: 6 cm by 7 cm
Height of the triangular prism tent: 12 cm
Rectangular face dimensions: 4 cm by 7 cm
1. Area of base triangular face = 0.5 * 6 * 7 = 21 cm²
2. Area of top triangular face = 0.5 * 6 * 7 = 21 cm²
3. Area of the rectangular face = 4 * 7 = 28 cm²
Total surface area = 2 * (Area of base triangular face + Area of top triangular face) + Area of rectangular face
Total surface area = 2 * (21 + 21) + 28
Total surface area = 2 * 42 + 28
Total surface area = 84 + 28
Total surface area = 112 cm²
Since the piece of fabric she purchased is 18 cm by 18 cm (324 cm²), the amount of fabric left over can be calculated as:
Fabric left over = Fabric purchased - Surface area of the tent
Fabric left over = 324 cm² - 112 cm²
Fabric left over = 212 cm²
Therefore, 212 cm² of fabric will be left over.
The closest option is not listed, but the most appropriate answer would be 212 cm².
To determine the surface area of the triangular prism (wedge of cheese), we need to calculate the areas of each face and sum them up.
Given:
Bottom face (triangular face) dimensions: 13 cm (base) and 9 cm (height)
Top face (triangular face) dimensions: 5 cm (base) and 9 cm (height)
Rectangular face dimensions: 12 cm (length) and 13 cm (height)
1. Area of bottom triangular face = 0.5 * 13 * 9 = 58.5 cm²
2. Area of top triangular face = 0.5 * 5 * 9 = 22.5 cm²
3. Area of rectangular face = 12 * 13 = 156 cm²
Total surface area = 2 * (Area of bottom triangular face + Area of top triangular face) + Area of rectangular face
Total surface area = 2 * (58.5 + 22.5) + 156
Total surface area = 2 * 81 + 156
Total surface area = 162 + 156
Total surface area = 318 cm²
Therefore, to cover the wedge of cheese with plastic wrap, 318 cm² of plastic wrap is needed.
The closest option is not listed, but the most appropriate answer would be 318 cm².
To find the surface area of the tent shaped as a triangular prism, we need to calculate the areas of each face and sum them up.
Given that the base of the triangular prism has dimensions of 18 cm by 18 cm and the height of the triangular prism is not provided, we can't accurately calculate the surface area.
However, if we assume that the height of the triangular prism is the same as the base's length, the surface area can be calculated. In this case, we'll assume the height of the prism is 18 cm.
1. Area of the base triangular face = 0.5 * 18 * 18 = 162 cm²
2. Area of the top triangular face = 0.5 * 18 * 18 = 162 cm²
3. Area of the three rectangular faces = Perimeter of the base * height = 3 * 18 * 18 = 972 cm²
Total surface area = 2 * (Area of the triangular face) + Area of the rectangular faces
Total surface area = 2 * (162 + 162) + 972
Total surface area = 648 cm²
Therefore, to cover the tent-shaped triangular prism with fabric, 648 cm² of fabric will be needed.
Since she purchased a piece of fabric with an area of 18 cm x 18 cm (324 cm²), the fabric will be insufficient.
There is no option representing how much fabric is left over, but the appropriate answer considering the fabric she purchased is 324 cm².