Q:

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. square inches 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. square inches

Accepted Solution

A:
Answer:  The smallest possible area of the tabletop=[tex]113\text{ square inches}[/tex]The largest possible area of the tabletop =[tex]1662\text{ square inches}[/tex]Step-by-step explanation:Given: The minimum radius of the tabletop = 6 inchesThe maximum radius of the tabletop = 23 inchesWe know that the area of circle is given by :-[tex]A=\pi r^2[/tex], where r is the radius of the circle.Now, the smallest possible area of the tabletop that will fit on Timothy’s table is given by :-[tex]A_s=(3.14159265359) (6)^2=113.097335529\approx113\text{ square inches}[/tex]The largest possible area of the tabletop that will fit on Timothy’s table is given by :-[tex]A_s=(3.14159265359) (23)^2=1661.90251375\approx1662\text{ square inches}[/tex]