A hot water heater measures 20" in diameter. What is the area of a metal base for the water heater, assuming a four-inch overhang for the base beyond the edge of the heater? (Round to the nearest tenth.)

615.44

20 + 8 = 28" diameter

A = pi * r^2

A = 3.14 * 14^2

To find the area of the metal base for the water heater, we need to calculate the area of a circle with a diameter of 20 inches, including the four-inch overhang.

The formula for the area of a circle is:

A = πr^2

Where A is the area and r is the radius of the circle.

First, let's find the radius. The radius is half the diameter, so:

r = 20 / 2 = 10 inches

Next, let's calculate the area of the circle with the radius of 10 inches:

A = π * 10^2
A ≈ 3.14 * 100
A ≈ 314 square inches

Now, let's add the four-inch overhang to the diameter:

Diameter with overhang = 20 + 2 * 4
Diameter with overhang = 20 + 8
Diameter with overhang = 28 inches

Now, let's find the radius of the circle with the overhang:

r = 28 / 2
r = 14 inches

Finally, let's calculate the area of the circle with the radius of 14 inches:

A = π * 14^2
A ≈ 3.14 * 196
A ≈ 615.44 square inches

Therefore, the area of the metal base for the water heater, assuming a four-inch overhang, is approximately 615.44 square inches.

To find the area of the metal base for the water heater, we first need to find the diameter of the base. Since the base has a four-inch overhang beyond the edge of the heater, we add twice the overhang (8 inches) to the diameter of the heater.

The diameter of the base will be:
Diameter of base = Diameter of heater + 2 × Overhang
= 20 inches + 2 × 4 inches
= 20 inches + 8 inches
= 28 inches

Now that we have the diameter of the base, we can calculate the area of the circular base using the formula for the area of a circle.

Area of base = π × (Radius of base)^2

To find the radius, we divide the diameter by 2:
Radius of base = Diameter of base / 2
= 28 inches / 2
= 14 inches

Now we can calculate the area of the base:
Area of base = π × (14 inches)^2
≈ 3.14 × 196 inches^2
≈ 615.44 inches^2

Therefore, the area of the metal base for the water heater, assuming a four-inch overhang, is approximately 615.4 square inches (rounded to the nearest tenth).