Problem Bank - 2D & 3D Geometry
Access custom-built, exam-style problems for 2d & 3d geometry. Each problem has a full solution and mark-scheme, as well as AI grading and support.
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A spherical white blood cell appears as a circle with circumference 6π×10−5m.
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Write down the radius of the cell.
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Find the volume of the cell, giving your answer in the form π(a×10k)m3, where a<10 and k∈Z.
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The points P and Q lie on a circle with center O and radius r such that PO^Q=2 radians.
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The perimeter of the shaded region is 7π.
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Find the value of r.
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Hence find the area of the region inside the circle that is not shaded.
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A tunnel is being dug through a mountain in a straight line. The cross sectional shape of the tunnel is shown in the diagram below.
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The shape consists of a rectangle ABCD with width AB=30m and height BC=8m, and a circular sector centered halfway between D and C at X between A and B.
Find, to three significant figures:
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The angle BX^C, in degrees.
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The angle BX^A, in radians.
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The arc length AB.
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The area of the tunnel's cross section.
The planned length of the tunnel is 2.3km.
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Find the volume that must be excavated (dug out) from the mountain.
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A chocolate ball is formed from a spherical shell with diameter d and thickness 2mm. The shell is filled on the inside with 3cm3 of caramel.
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Show that d=2.19cm.
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Hence find the volume of the chocolate shell.
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