What is the surface area required to cover a cylinder's lateral area and its top base in square inches?
To find the surface area of a cylinder, you need to calculate the sum of the lateral area and the area of its top base. Let's break it down step-by-step.
1. Find the lateral area of the cylinder:
- The lateral area of a cylinder is found by multiplying the height of the cylinder (h) by the circumference of the base (C).
- The formula for the lateral area of a cylinder is: Lateral Area = h * C.
- The circumference of the base (C) can be calculated by multiplying the diameter (d) of the base by pi (π). Therefore, C = d * π.
2. Find the area of the top base:
- The area of a circle is calculated by multiplying the square of the radius (r) by pi (π). Therefore, Area = r^2 * π.
- Since the top base has the same dimensions as the bottom base, the formula for the area of the top base is the same as the area of the bottom base.
3. Add the lateral area and the area of the top base to get the total surface area:
- Total Surface Area = Lateral Area + 2 * Area of the Top Base.
- The lateral area is only added once because it covers the entire curved surface of the cylinder, while the area of the top base is counted twice because it appears on both the top and bottom of the cylinder.
By following these steps and using the appropriate formulas, you can calculate the surface area required to cover a cylinder's lateral area and both its top and bottom base.
To find the surface area required to cover a cylinder's lateral area and top base, you need to calculate the lateral surface area and the surface area of the top base separately, and then add them together.
1. Lateral Surface Area:
The lateral surface area of a cylinder is calculated by multiplying the height of the cylinder by the circumference of its base. The formula for the lateral surface area (LA) is given as:
LA = 2πrh, where r is the radius of the base and h is the height of the cylinder.
2. Surface Area of Top Base:
The surface area of the top base is calculated by multiplying the area of a circle (πr²) by 1 since there is only one top base. The formula for the surface area of the top base (TA) is given as:
TA = πr², where r is the radius of the base.
3. Add the Lateral Surface Area and Surface Area of Top Base:
To find the total surface area required, you add the lateral surface area and the surface area of the top base together:
Total surface area = LA + TA
Therefore, the formula for the total surface area (SA) required to cover a cylinder's lateral area and top base is:
SA = LA + TA = 2πrh + πr²
Now you can use the formula and the given measurements (radius and height) to calculate the surface area required in square inches.