Acorner shelf is 1/4 of a circle and has a radius of 10.5 inches. enter the area of the shelf in square inches. round your answer to the nearest hundredth. i know the answers are 86.55 - 86.68 but i don't know how it got that answer

The area of shelf is:

                        86.55 square inches.

We are given that the corner shelf is 1/4 of a circle.

Hence, the area of the shelf is also 1/4 times the area of a circle.

We know that the Area of circle with radius ''r'' is given by:

Area=πr²

Radius here is: r=10.5 inches.

Hence, the area of circle= π×(10.5)²

                                        =346.185 square inches.

Hence, area of shelf is: Area of circle/4

                                   = 346.185/4

                                   = 86.54625

Hence, round to the nearest hundredth the area of shelf is:

                                    86.55 square inches.

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step-by-step explanation: