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.