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A spherical white blood cell appears as a circle with circumference 6π×10−5m.
Write down the radius of the cell.
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.
Find the value of r.
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:
The angle BX^C, in degrees.
The angle BX^A, in radians.
The arc length AB.
The area of the tunnel's cross section.
The planned length of the tunnel is 2.3km.
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.
Show that d=2.19cm.
Hence find the volume of the chocolate shell.
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