A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?
Georgia Milestones Grade 7 Mathematics Formula Sheet
(1 point)
Responses
287 centimeters squared
287 centimeters squared
330 centimeters squared
330 centimeters squared
810 centimeters squared
810 centimeters squared
240 centimeters squared
240 centimeters squared
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To find the surface area of the triangular prism shaped wedge of cheese, we need to find the area of each of the five faces: two triangular faces and three rectangular faces.
Let's assign some values:
Base of the triangle = 10 cm
Height of the triangle = 8 cm
Height of the prism = 12 cm
Area of each triangle = (1/2) * base * height
Area of each triangle = (1/2) * 10 cm * 8 cm
Area of each triangle = 40 cm²
Area of the two triangular faces = 2 * 40 cm²
Area of the two triangular faces = 80 cm²
Area of each rectangular face = base * height
Area of each rectangular face = 10 cm * 12 cm
Area of each rectangular face = 120 cm²
Area of the three rectangular faces = 3 * 120 cm²
Area of the three rectangular faces = 360 cm²
Total surface area = 80 cm² (triangular faces) + 360 cm² (rectangular faces)
Total surface area = 440 cm²
Therefore, 440 cm² of plastic wrap is needed to cover the wedge of cheese. None of the provided options match this calculation.
pick one of the answers
240 centimeters squared
a more interesting problem would be to model a real wedge of cheese, cut from a round wheel. If we let
r = radius of wheel
h = height of the wheel
θ = angle subtended by the wedge, then
volume = 1/2 r^2 θ h
surface area = 2(1/2 r^2 θ) + 2(rh) + rθh
That is indeed a more interesting and realistic problem to model a wedge of cheese cut from a round wheel. The formulas you provided for the volume and surface area of the wedge are correct and can be derived from the geometry of a circular sector and the lateral and top surfaces of the resulting wedge.
By using these formulas, we can accurately calculate the volume and surface area of a wedge of cheese based on the radius of the wheel, height of the wheel, and angle subtended by the wedge. Thank you for sharing this more detailed and practical approach.