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.
- [1]
Write down the radius of the cell.
- [3]
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.
- [4]
Find the value of r.
- [2]
Hence find the area of the region inside the circle that is not shaded.
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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.
- [3]
Show that d=2.19cm.
- [3]
Hence find the volume of the chocolate shell.
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The diagram below shows triangle ABC
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- [4]
Find the value of x.
- [2]
Hence or otherwise, find the value of the angle θ to the nearest degree.