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If the diameter of the circle is , what is the circumference and area of the figure?
Answer
384.3k+ views
Hint: Here in this question we want to find the area and circumference of a circle whose diameter is given to us as . To find the area of a circle, we have a standard formula, . Also, we have a standard formula for finding the circumference of a circle when we are provided with the radius of the circle, . We know the value of and the value of radius is given to us in the question itself. We substitute known values and determine the area of a circle using the formula.
Complete step by step answer:
The circle is a two dimensional figure and we have to determine the area, where the area is the region or space occupied by the circular field. To determine the area of a circle we have the standard formula where r represents the radius. In the given question, we are given the length of the diameter in centimetres. So, we will first find the radius using .
So,
So, we will get the area of the circle using the formula in the unit square centimetres.
To find the area of a circle, we use formula . The radius of the circle is .
By substituting, we get,
Therefore the area of a circle with a radius centimetres is .We can substitute the value of to find the area and we can simplify further.Substituting the value of , we have,
Further simplifying the calculations, we have,
On further simplification and representing it in decimal expression, we have,
Hence the area of a circle whose diameter is centimetres is .
Now, the circumference of the circle can be calculated using the formula by substituting the value of the radius of the circle given in the question itself.
So, we get,
Putting the value of , we get,
Therefore, the circumference of a circle with a diameter centimetre is .
Note: The circle is a two-dimensional figure and we have to determine the area, where the area is the region or space occupied by the circular field. The area of a circle is defined as the region occupied by the circular region. The radius is denoted by r or R. Value of is approximately taken as . The radius of a circle is half of the value of the diameter. So, we have, .
Complete step by step answer:
The circle is a two dimensional figure and we have to determine the area, where the area is the region or space occupied by the circular field. To determine the area of a circle we have the standard formula
So,
So, we will get the area of the circle using the formula in the unit square centimetres.
To find the area of a circle, we use formula
By substituting, we get,
Therefore the area of a circle with a radius
Further simplifying the calculations, we have,
On further simplification and representing it in decimal expression, we have,
Hence the area of a circle whose diameter is
Now, the circumference of the circle can be calculated using the formula
So, we get,
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Putting the value of
Therefore, the circumference of a circle with a diameter
Note: The circle is a two-dimensional figure and we have to determine the area, where the area is the region or space occupied by the circular field. The area of a circle is defined as the region occupied by the circular region. The radius is denoted by r or R. Value of
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