A circular hot tub located near the middle of a rectangular patio has a

diameter of 48 inches. The patio measures 11 feet by 6 feet. What is the area

of the patio that is not covered by the hot tub? Round to the nearest tenth.

The area of the patio without the tub is 53.44 ft²

Step-by-step explanation:

In order to calculate the area of the patio that is not covered by the hot tub we need to calculate the total area of the patio and subtract it by the area of the tub. Since the patio is rectangular it's area is given by "area = length*width" and the area of the tub is given by "area = pi*r²".

area patio = length*width = 11*6 = 66 ft²

area tub = pi*r² = pi * (48/2) ² = pi * (24) ² = 1,808.64 in²

To compare the area we need to convert the areas to the same unit, to do that we will convert the area of the tub from in² to ft², in order to do that we need to divide the value by 144. We have:

area tub = 1,808.64/144 = 12.56 ft²

The area of the patio without the tub is:

x = area patio - area tub = 66 - 12.56 = 53.44 ft²