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Timothy built a base for a circular tabletop. The base can support a tabletop with a radius of at least 6 inches, but not more than 23 inches. What is the smallest possible area of the tabletop that will fit on Timothy’s table base? Round the answer to the nearest whole square inch. What is the largest possible area of the tabletop that will fit on Timothy’s table base? Round the answer to the nearest whole square inch.

Respuesta :

calculista

Let

r------> the radius of the circular tabletop

we know that

[tex]r\geq 6\ in[/tex]

[tex]r\leq23\ in[/tex]

so

[tex]6\ in \leq r \leq 23\ in[/tex]

The area of a circle is equal to

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

where

r is the radius of the circle

Part a) What is the smallest possible area of the tabletop that will fit on Timothy’s table base?

we know that

the smallest possible area of the tabletop is for [tex]r=6\ in[/tex]

Substitute the value  of r in the formula

[tex]A=\pi 6^{2}[/tex]

[tex]A=113.09\ in^{2}[/tex]

Round to the nearest whole square inch

so

[tex]A=113\ in^{2}[/tex]

therefore

the answer part a) is

the smallest possible area of the tabletop is [tex]113\ in^{2}[/tex]

Part b) What is the largest possible area of the tabletop that will fit on Timothy’s table base?

we know that

the largest possible area of the tabletop is for [tex]r=23\ in[/tex]

Substitute the value  of r in the formula

[tex]A=\pi 23^{2}[/tex]

[tex]A=1,661.90\ in^{2}[/tex]

Round to the nearest whole square inch

so

[tex]A=1,662\ in^{2}[/tex]

therefore

the answer part b) is

the largest possible area of the tabletop is [tex]1,662\ in^{2}[/tex]

The smallest possible area of the tabletop is [tex]113\, inches^{2}[/tex].

The largest possible area of the tabletop is [tex]1662\, inches^{2}[/tex]

Given: The radius (r) of a circular tabletop

[tex]6\leq r\leq 23[/tex]

The area of a circle is given by

[tex]Area=\pi r^{2}[/tex]

Where, r is the radius of a circular tabletop

(1) For the smallest possible area of the tabletop

r = 6 inches

[tex]Area = \pi r^{2} \\Area=3.14\times 6^{2} \\Area=113.097\,inches^{2}[/tex]

Round to the nearest whole square inch

[tex]Area=113\,inches^{2}[/tex]

Therefore, the smallest possible area of the tabletop is [tex]113\, inches^{2}[/tex].

(2) For the largest possible area of the tabletop

r = 23 inches

[tex]Area=\pi \times (23)^{2} \\Area=3.14 \times 529\\Area=1661.90\,inches^{2}[/tex]

Round to the nearest whole square inch

[tex]Area=1662\,inches^{2}[/tex]

Therefore, the largest possible area of the tabletop is [tex]1662\, inches^{2}[/tex]

For more information:

https://brainly.com/question/23328170

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