A hot water heater measures 20" in diameter. What is the area of a metal base for the water heater, assuming a two-inch overhang for the base beyond the edge of the heater?
A = pi * r^2
A = 3.14 * 12^2
A = ?
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 plus the area of a ring created by the two-inch overhang.
1. Calculate the radius of the water heater:
The diameter is 20 inches, so the radius is half of the diameter, which is 20 inches / 2 = 10 inches.
2. Calculate the area of the large circle:
The formula for the area of a circle is A = πr^2, where A represents the area and r represents the radius.
Plugging in the values, we get A = π * (10 inches)^2.
3. Calculate the radius of the base with overhang:
Since the base has a two-inch overhang, we need to increase the radius by two inches:
New radius = 10 inches + 2 inches = 12 inches.
4. Calculate the area of the smaller circle:
The formula for the area of a circle is still A = πr^2, but this time we're using the new radius.
Plugging in the values, we get A = π * (12 inches)^2.
5. Subtract the smaller circle's area from the larger circle's area to get the area of the ring:
A_ring = A_large circle - A_small circle.
Combining these steps, we have:
A_ring = (π * (10 inches)^2) - (π * (12 inches)^2)
To find the area of the metal base for the water heater, we need to calculate the area of a circular shape. The formula to find the area of a circle is given by:
A = πr^2
Where A is the area and r is the radius of the circle.
In this case, the diameter of the water heater is given as 20 inches. We need to calculate the radius by dividing the diameter by 2:
Radius (r) = Diameter / 2 = 20" / 2 = 10"
Now, since the base has a two-inch overhang beyond the edge of the heater, we need to add this overhang to the radius. The new radius will be the sum of the radius and the overhang:
New Radius = Radius + Overhang = 10" + 2" = 12"
Now we can plug this new radius value into the formula to calculate the area:
A = πr^2 = π(12")^2
To find the area of the base, we can use the value of π as approximately 3.14:
A = 3.14 * (12")^2
A = 3.14 * 144"
A = 452.16 square inches
Therefore, the area of the metal base for the water heater, assuming a two-inch overhang, is 452.16 square inches.