Ahomeowner is building a circular fire pit in his backyard. he plans to outline the pit with bricks and cover the space inside the pit with sand. the homeowner has decided to build the pit with a diameter of 3 feet.

in order to know how many bricks to buy, the homeowner must know the distance around the outside of the pit. calculate both the exact distance and the approximate distance.

in order to know how much sand to buy, the homeowner must know how much space needs to be covered inside the pit. calculate both the exact area and the approximate area.

Circumference(C) and Area(A) of the circle is given by:

where, r is the radius of the circle.

As per the statement:

A homeowner is building a circular fire pit in his backyard.

The homeowner has decided to build the pit with a diameter of 3 feet.  

⇒Diameter(d) = 3 feet

We know that:

diameter(d) = 2r

then;

Divide both sides by 2 we have;

or

r = 1.5 ft

In order to know how many bricks to buy, the homeowner must know the distance around the outside of the pit.

We have to find  both the exact distance and the approximate distance.

For exact distance:

Substitute the value of r we have;

Simplify:

feet

For approximate distance:

Use

then;

ft

Therefore, the exact distance is feet and the approximate distance is, 9 ft.

In order to know how much sand to buy, the homeowner must know how much space needs to be covered inside the pit.

we have to find  both the exact area and the approximate area.

For exact area:

Substitute the value of r we have;

Simplify:

For approximate area:

Use

then;

Simplify:

Therefore, the exact area is, and the approximate area is, 7 square feet

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step-by-step explanation: