Determine the total surface area of the cylinder. (Use 3.14 for π.) (1 point) Responses 100 square centimeters 100 square centimeters 500 square centimeters 500 square centimeters 707 square centimeters 707 square centimeters 785 square centimeters radius is 5 height is 20
Total surface area of a cylinder = 2πr(r + h)
Given:
r = 5
h = 20
Total surface area = 2 * 3.14 * 5(5 + 20)
Total surface area = 2 * 3.14 * 5(25)
Total surface area = 2 * 3.14 * 125
Total surface area = 2 * 392.5
Total surface area = 785 square centimeters
Therefore, the total surface area of the cylinder is 785 square centimeters.
Determine the total surface area of the triangular prism. (1 point) Responses 126 square centimeters 126 square centimeters 252 square centimeters 252 square centimeters 504 square centimeters 504 square centimeters 6,480 square centimeters 12cm, 15cm, 4cm, 9cm.
Total surface area of a triangular prism = 2 * Base area + Lateral area
To find the base area of the triangular prism:
Base area = (1/2) * base * height
Base area = (1/2) * 12 * 15
Base area = (1/2) * 180
Base area = 90 square centimeters
Now, to find the lateral area of the triangular prism:
Lateral area = perimeter of base * height
Perimeter of base = 12 + 15 + 9 = 36
Lateral area = 36 * 4
Lateral area = 144 square centimeters
Total surface area = 2 * 90 + 144
Total surface area = 180 + 144
Total surface area = 324 square centimeters
Therefore, the total surface area of the triangular prism is 324 square centimeters.
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To find the total surface area of a triangular prism, we need to calculate the lateral surface area and the base area separately and then sum them up.
Given:
Base dimensions: 12 cm and 15 cm
Height of the prism: 9 cm
The lateral surface area of a prism can be calculated using the formula: perimeter of the base * height
Perimeter of the base = sum of the three sides of the base triangle
Perimeter of the base = 12 + 15 + 9 = 36 cm
Lateral surface area = 36 cm * 9 cm = 324 square cm
Now, let's calculate the base area of the triangular prism:
Base area = (1/2) * base * height
Base area = (1/2) * 12 cm * 15 cm = 90 square cm
Total surface area of the triangular prism = 2 * base area + lateral surface area
Total surface area = 2 * 90 cm + 324 cm
Total surface area = 180 cm + 324 cm
Total surface area = 504 square centimeters
Therefore, the total surface area of the triangular prism is 504 square centimeters.
Determine the total surface area of the rectangular prism. (1 point) Responses 147 square inches 147 square inches 270 square inches 270 square inches 294 square inches 294 square inches 540 square inches 10in, 9in, 3in,
To find the total surface area of a rectangular prism, we need to calculate the area of all six faces of the prism and then sum them up.
Given:
Length = 10 inches
Width = 9 inches
Height = 3 inches
The formula for the total surface area of a rectangular prism is:
Total Surface Area = 2lw + 2lh + 2wh
Substitute the given values:
Total Surface Area = 2(10*9) + 2(10*3) + 2(9*3)
Total Surface Area = 2(90) + 2(30) + 2(27)
Total Surface Area = 180 + 60 + 54
Total Surface Area = 294 square inches
Therefore, the total surface area of the rectangular prism is 294 square inches.
Determine the total area of the THREE lateral faces of this triangular prism. (1 point) Responses 48 square inches 48 square inches 96 square inches 96 square inches 188 square inches 188 square inches 448 square inches 448 square inches 10in, 8in, 10in, 14in, 12in.
To find the total area of the three lateral faces of the triangular prism, we need to calculate the area of each lateral face and then sum them up.
Given:
Base dimensions: 10 inches and 8 inches
Height of the prism: 14 inches
Lateral faces are the three faces that are not the bases.
The lateral faces of a triangular prism are rectangles with a length equal to the perimeter of the base and a height equal to the height of the prism.
Perimeter of the triangle = sum of the three sides = 10 + 8 + 10 = 28 inches
Lateral face area = perimeter of the base * height
Lateral face area = 28 inches * 14 inches = 392 square inches
Since there are three lateral faces, the total area of the three lateral faces would be:
Total lateral face area = 3 * 392 square inches = 1176 square inches
Therefore, the total area of the three lateral faces of the triangular prism is 1176 square inches.