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A circular tabletop has a radius of 24 inches.

What is the area of the tabletop, to the nearest square inch? Use 3.14 for [tex]$\pi$[/tex].

A. 75 in[tex]$^2$[/tex]
B. 151 in[tex]$^2$[/tex]
C. 1809 in[tex]$^2$[/tex]
D. 7235 in[tex]$^2$[/tex]

Sagot :

To determine the area of a circular table top with a radius of 24 inches, we need to use the formula for the area of a circle:

[tex]\[ A = \pi r^2 \][/tex]

Where:
- \( A \) is the area of the circle
- \( \pi \) is a constant approximately equal to 3.14
- \( r \) is the radius of the circle

Given that the radius (\( r \)) is 24 inches, we can substitute this value into the formula:

[tex]\[ A = 3.14 \times (24^2) \][/tex]

First, calculate the square of the radius:

[tex]\[ 24^2 = 576 \][/tex]

Next, multiply this by \( \pi \):

[tex]\[ A = 3.14 \times 576 \][/tex]

After performing the multiplication, we get:

[tex]\[ A = 1808.64 \, \text{square inches} \][/tex]

Rounding this to the nearest square inch, we get:

[tex]\[ A \approx 1809 \, \text{square inches} \][/tex]

Therefore, the area of the table top is approximately 1809 square inches. Hence, the correct answer is:

[tex]\[ \boxed{1809 \, \text{in}^2} \][/tex]