Use the image to answer the question.
An illustration shows a 3 D triangular prism with the triangular face as a right triangle. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measure 19 inches and 8 inches. The perpendicular side of the triangular face measures 6 inches and the hypotenuse measures 10 inches.
The diagram represents a model of a ramp the skateboard club wants to create at the neighborhood skate park. If one pint of paint covers 200 square inches, how many pints of paint will the club need to purchase? Paint is only sold in whole pints.
First, we need to calculate the total surface area of the triangular prism. The formula to calculate the surface area of a triangular prism is A = 2B + Ph, where B is the area of the base (the triangular face), P is the perimeter of the base, and h is the height of the prism.
First, let's calculate the area of the triangular face:
Area of a triangle = (1/2) * base * height
Area = (1/2) * 8 * 6 = 24 square inches
Next, let's calculate the perimeter of the base:
Perimeter = 8 + 6 + 10 = 24 inches
Now, let's calculate the total surface area of the triangular prism:
A = 2B + Ph
A = 2(24) + 24(19)
A = 48 + 456
A = 504 square inches
Since 1 pint of paint covers 200 square inches, we divide the total surface area by 200 to find out how many pints of paint are needed:
504 / 200 = 2.52
Since paint is only sold in whole pints, the skateboard club will need to purchase 3 pints of paint.
Find the surface area of a cube with sides measuring 11 meters.(1 point)
Responses
66 m2
66 m squared
726 m2
726 m squared
132 m2
132 m squared
121 m2
To find the surface area of a cube, you need to calculate the area of all six faces of the cube and add them together.
The formula for the surface area of a cube is: 6 * side^2
Given that the sides of the cube measure 11 meters, you plug this value into the formula:
Surface Area = 6 * 11^2
Surface Area = 6 * 121
Surface Area = 726 m^2
Therefore, the correct answer is:
726 m2
Cherese 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?(1 point)
Responses
426 in.2
426 in. squared
406 in.2
406 in. squared
54 in.2
54 in. squared
446 in.2
First, let's calculate the surface area of the box. A box has 6 faces, but two of them will not be used in this case as the lid and bottom of these boxes are not needed. Thus, the surface area will be the area of the 4 faces that will be used to build the box.
The formula to find the surface area of a rectangular prism is: 2lw + 2lh + 2wh, where l, w, and h are the length, width, and height of the prism.
Given:
Length (l) = 10 inches
Width (w) = 9 inches
Height (h) = 7 inches
Now, substituting the values into the formula:
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
If Cherese purchases 500 square inches of cardboard and the surface area of the box is 446 square inches, this means there will be 500 - 446 = 54 square inches of cardboard left over.
Therefore, the correct answer is:
54 in.2
Use the image to answer the question.
An illustration shows a 3 D triangular prism with the triangular face as a right triangle. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measures 12 centimeters and 9 centimeters. The perpendicular side of the triangular face measures 5 centimeters and the hypotenuse measures 13 centimeters.
A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?
To find the total surface area of the triangular prism (wedge of cheese in this case), we need to calculate the sum of the areas of all its faces.
The formula to find the surface area of a triangular prism is: A = 2B + Ph, where B is the area of the triangular base, P is the perimeter of the base, and h is the height of the prism.
Given:
Base area (B) = (1/2) * 9 * 5 = 22.5 cm²
Perpendicular side (P) = 9 + 5 + 13 = 27 cm
Prism height (h) = 12 cm
Now, substitute the values into the formula:
Surface Area = 2(22.5) + 27(12)
Surface Area = 45 + 324
Surface Area = 369 cm²
Therefore, 369 cm² of plastic wrap is needed to cover the wedge of cheese.
Use the image to answer the question.
An illustration shows a 3 D triangular prism with the triangular face as a right triangle. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measures 12 centimeters and 9 centimeters. The perpendicular side of the triangular face measures 5 centimeters and the hypotenuse measures 13 centimeters.
A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?
(1 point)
Responses
240 cm2
240 cm squared
330 cm2
330 cm squared
810 cm2
810 cm squared
287 cm2
To find the total surface area of the triangular prism (in the shape of a wedge of cheese in this case), we need to calculate the sum of the areas of all its faces.
The formula to find the surface area of a triangular prism is: A = 2B + Ph, where B is the area of the triangular base, P is the perimeter of the base, and h is the height of the prism.
Given:
Base area (B) = (1/2) * 9 * 5 = 22.5 cm²
Perpendicular side (P) = 9 + 5 + 13 = 27 cm
Prism height (h) = 12 cm
Now, substitute the values into the formula:
Surface Area = 2(22.5) + 27(12)
Surface Area = 45 + 324
Surface Area = 369 cm²
Therefore, 369 cm² of plastic wrap is needed to cover the wedge of cheese.
None of the provided options match this calculated result. 369 cm² is the correct answer.
Use the image to answer the question.
An illustration shows a 3 D triangular prism. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measures 12 centimeters and 4 centimeters. The perpendicular height h measures 6 centimeters, and the sides of the triangular face measures 7 centimeters.
Jordan purchased a piece of fabric that is 18 cm by 18 cm in order to make a tent for her little sister’s dolls. Using the dimensions for the tent shaped as a triangular prism, how much fabric will be left over?
(1 point)
Responses
240 cm2
240 cm squared
84 cm2
84 cm squared
324 cm2
324 cm squared
184 cm2