Answer :
To calculate the surface area of a cylindrical pencil holder, we find the areas of the two circular bases and the side of the cylinder and add them together. The total surface area calculated is 133.45 square inches, and the closest answer choice provided is (b) 130.9 square inches.
The question is asking for the surface area of a cylindrical pencil holder. To find the surface area of a cylinder, we need to calculate the area of the two circular bases and the area of the side, which is a rectangle that wraps around the bases. The formula for the area of a circle is
=
[tex]^2,[/tex] and the area of the rectangle is the circumference of the base times the height of the cylinder (C*h, where C = 2*
).
- First, we calculate the radius of the base by dividing the diameter by 2, which gives us 2.5 inches.
- Next, we find the area of one base:
=
[tex]^2 = 3.14 * (2.5 inches)^2 = 19.625[/tex] square inches. Since there are two bases, we double this to get 39.25 square inches for both bases together. - We then calculate the circumference of the base (C) which is C = 2*
= 2 * 3.14 * 2.5 inches = 15.7 inches. - Finally, we calculate the area of the side by multiplying the circumference by the height: 15.7 inches * 6 inches = 94.2 square inches.
- Adding the area of the bases and the side together gives us 39.25 square inches + 94.2 square inches = 133.45 square inches, which is the surface area of the cylindrical pencil holder.
The closest answer choice to our calculation is (b) 130.9 square inches, so there might be a slight discrepancy due to the use of an approximate value of . However, as none of the answers are exactly 133.45 square inches, it is important to check the specifics of the question, as it's possible that a more precise value of or a different rounding convention might lead to an exact match with one of the provided answer choices.
