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Geometry SY222113-3003
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Below is the side view of a uniformly tapering wedge. The wedge narrows uniformly towards its right end.
The thickness at the left end is 20.0 mm, and at the right end, it is 10.0 mm. The length of the wedge L is 245.9 mm.
What is the thickness of the wedge at point x, which is 24.9 mm from the left end of the wedge?
Provide the result to an accuracy of 0.1 mm.
Calculate the area of the shaded part of the circular disk.
Provide the answer to two decimal places.
A circular sector-shaped sheet is bent into a circular cone. What is the volume of the cone thus formed, given that the radius of the sector is 82.8 mm and the central angle is 57.5°?
Provide the answer in to one decimal place.
The formula for the volume of a circular cone:
The map is drawn to a scale of 1:5000. On the map, the distance between two points is 276 mm. Determine the actual distance between these points in nature in meters.
Provide the answer to an accuracy of 1 meter.
Calculate the area of the quadrilateral in the picture, given that the length of the bottom side in the picture is 131m and the length of the left side is 98m, and 45°.
Provide the answer in square meters as an integer.
The ends of the open trough shown in the picture are isosceles trapezoids, and the other faces are rectangles. The given dimensions are the internal dimensions of the trough. What is the volume of the trough?
Provide the answer as an integer.
The bottom of the open trough shown in the picture is rectangular, but the other faces are trapezoids. What is the volume of the trough?
Provide the answer as an integer.
Calculate the area of the shaded part of the circular disk.
Provide the answer to two significant figures.
Calculate the area of the trapezoid in the picture.
Provide the answer in square meters to three significant figures.
In Spectre's control room, there is a display with a map showing a light point that represents a car's movement on the road. The map scale is 1:50,000. At what speed does the light point move on the map when it represents a car traveling at 120 km/h?
Provide your answer in units of mm/s to two decimal places.