Final answer:
The total surface area of a cylindrical candle with a diameter of 4 inches and a height of 7 inches is approximately 100.48 square inches.
Step-by-step explanation:
The total surface area of a cylindrical candle can be found by adding the areas of the two bases and the lateral surface area. The formula for the lateral surface area of a cylinder is given by:
Lateral surface area = 2πrh
Given that the diameter is 4 inches, the radius (r) is half of that, which is 2 inches. And the height (h) of the cylinder is 7 inches.
So, the lateral surface area of the candle is: 2π(2 inches)(7 inches) = 28π square inches.
Now, we need to find the areas of the two bases, which are circles.
The formula for the area of a circle is given by:
Area = πr^2
For the candle, the radius (r) is 2 inches. So, the area of each base is: π(2 inches)^2 = 4π square inches.
Therefore, the total surface area of the candle is the sum of the lateral surface area and the areas of the two bases:
Total surface area = 28π + 4π = 32π square inches.
Since the value of π is approximately 3.14, we can approximate the total surface area to be 32(3.14) square inches, which is approximately 100.48 square inches.