Ming has 12 unsharpened pencils bundled in the shape of a cylinder. If the diameter is 0.5 cm and the length is 19 cm, what is the surface area of Ming’s bundle of pencils? Use 3.14 for π and round to the nearest tenth
To find the surface area of the bundle of pencils, we will first find the surface area of the side of the cylinder and the two bases.
The lateral surface area of a cylinder can be calculated using the formula: 2πrh, where r is the radius and h is the height.
Given that the diameter is 0.5 cm, the radius (r) would be half of the diameter, so r = 0.25 cm.
The height (h) of the cylinder is 19 cm.
Lateral Surface Area = 2 * 3.14 * 0.25 * 19 = 11.83 cm²
Now, let's calculate the area of the two bases of the cylinder.
The area of a circle is given by the formula: πr².
Base Area = 3.14 * 0.25² = 0.19625 cm²
There are two bases, so the total area of the bases is:
2 * Base Area = 2 * 0.19625 = 0.3925 cm²
Now, to get the total surface area of the bundle of pencils, we add the lateral surface area and the base area:
Total Surface Area = Lateral Surface Area + 2 * Base Area
= 11.83 + 0.3925
= 12.2225 cm²
Therefore, the surface area of Ming’s bundle of pencils is 12.2 cm² when rounded to the nearest tenth.