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.

Let

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

we know that

so

The area of a circle is equal to

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

Substitute the value  of r in the formula

Round to the nearest whole square inch

so

therefore

the answer part a) is

the smallest possible area of the tabletop is

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

Substitute the value  of r in the formula

Round to the nearest whole square inch

so

therefore

the answer part b) is

the largest possible area of the tabletop is

The smallest possible area of the tabletop is .

The largest possible area of the tabletop is

Given: The radius (r) of a circular tabletop

The area of a circle is given by

Where, r is the radius of a circular tabletop

(1) For the smallest possible area of the tabletop

r = 6 inches

Round to the nearest whole square inch

Therefore, the smallest possible area of the tabletop is .

(2) For the largest possible area of the tabletop

r = 23 inches

Round to the nearest whole square inch

Therefore, the largest possible area of the tabletop is

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t = 3

step-by-step explanation:

put t = 3 in this expression :

(3²-1)(3²-2)(3² - 3)(3² - 4) = 8×7×6×5 = 56×30 = 1680