Question

Need help in geometry right answers only please give me now 25 points

Answer 1

What is the area of a circle with a diameter measuring 10 inches?
31.4 square cm
81.41 square cm
153.93 square cm
78.54 square cm

In solving this problem, let us recall the formula for the area of a circle:
We know that the formula for the area of a circle is given by:
A= (pi)(r^2)

Since in this problem, the diameter is given by 10 inches:
But diameter= radius(r) times 2
D= 2r
Thus;
r=5 inches

Substitute:
A= (pi)(5^2)
A=78.54 square inches

Convert inches to cm since the choices are in cm:
1 inch= 2.54 cm

78.54 inches(2.54 cm/1 inch)
A=199.49 square cm

Since the correct answer is not in the given choices, it can be assumed that the choices have a wrong label/unit. We can then say that the correct answer should be:

A=78.54 square inches
or
A=199.49 square cm

Answer 2

The area of the circle = π r² = π (d/2)²
Where r is the radius of the circle
And d is the diameter of the circle
d = 2r OR r = d/2
given d = 10 in ∴ r = d/2 = 10/2 = 5 in
∴ The area of the circle = π r² = π * 5² = 25π ≈ 78.54 in²

The correct answer is the fourth option 78.54

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very important note:
There is a mistake in the dimension of the answers.
The dimension of the given diameter is inch , while the dimensions of the answers is square cm.

If it is required to find the area in square cm
∵ 1 inch = 2.54 cm
∴ r = d/2 = 10/2 = 5 in = 5 * 2.54 cm = 12.7 cm

∴ Area = π r² = π * (12.7)² = 161.29π ≈ 506.7 square cm