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Answer :
To calculate the surface area of a cylinder, the formula involves finding the sum of the areas of the two bases and the lateral surface area. The cylindrical pencil holder's total surface area is approximately 130.9 square inches, closest to option b. Therefore, The correct answer is b. 130.9 square inches.
The question asks for the surface area of a cylindrical pencil holder with a base diameter of 5 inches and a height of 6 inches. To calculate the surface area of a cylinder, we need to find the areas of the two circular bases and the area of the cylindrical side (the lateral surface area).
First, we calculate the radius (r) of the cylinder which is half of the diameter. Thus, r = 5 inches / 2 = 2.5 inches. Next, we use the formula for the area of a circle (Area = \\\pi r^2\) to find the area of one base, and then multiply by 2 since there are two bases:
\Base Surface Area = 2 \\times \\pi \\times (2.5 inches)^2 = 2 \\times \\pi \\times 6.25 inches^2 = 2 \\times \\pi \\times 6.25 inches^2
The lateral surface area is the perimeter of the base times the height of the cylinder (Lateral Surface Area = 2 \\times \\pi \\times r \\times height). So for our pencil holder:
\Lateral Surface Area = 2 \\times \\pi \\times 2.5 inches \\times 6 inches = 2 \\times \\pi \\times 15 inches^2
Now we add the base surface area and the lateral surface area to get the total surface area:
\Total Surface Area = Base Surface Area + Lateral Surface Area= 2 \\times \\pi \\times 6.25 inches^2 + 2 \\times \\pi \\times 15 inches^2
After calculating using \\pi \\approx 3.14159, the total surface area is found to be:
\Total Surface Area = 2 \\times 3.14159 \\times 6.25 inches^2 + 2 \\times 3.14159 \\times 15 inches^2 \\approx 39.27 inches^2 + 94.25 inches^2 = 133.52 inches^2
So, the correct answer is closest to option b. 130.9 square inches.
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