WEBVTT
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Find, to the nearest tenth, the volume of a hemisphere given that the circumference of its great circle is 82π.
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A hemisphere is half a sphere, and its volume can be calculated using the formula two-thirds ππ cubed, where π is the radius of the hemisphere.
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The great circle is the base of the hemisphere, as shown in the diagram.
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The circumference of any circle can be calculated using the formula ππ.
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As weβre told the circumference of the great circle is 82π, then this is equal to ππ.
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Dividing both sides of this equation by π gives us 82 is equal to π.
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This means that the diameter of the great circle is 82 units.
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The radius is half the diameter, so this can be calculated by dividing 82 by two.
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This is equal to 41.
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We can now calculate the volume of the hemisphere by multiplying two-thirds by π by 41 cubed.
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Typing this into the calculator gives us 144347.804 and so on.
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As we need to round to the nearest tenth, the deciding number is the zero in the hundredths column.
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If the deciding number is less than five, we round down.
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The volume of the hemisphere to the nearest tenth is 144347.8.
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In this question, we donβt know the specific units.