please guys help me this question, how to solve it.
Calculate the total surface area of a hollow cylinder whose radius is 15 cm and height is 20 cm.
consider slicing down the side of the cylinder and unrolling the curved part. That is just a rectangle with the same height as the cylinder (h), and a width equal to the circumference (2πr).
So the area is just the inside plus the outside, which are the same, if the cylinder has essentially zero thickness.
A = 2*2πrh
As = 2(pi*r^2) + 2pi*r*h = Total surface area.
Convert r and h to meters.
Oops! the first term of my Eq does not exist, because the cylinder is hollow.
To calculate the total surface area of a hollow cylinder, we need to find the areas of both the curved surface and the two circular bases, and then add them together.
1. The curved surface area of a hollow cylinder can be calculated using the formula:
Curved Surface Area = 2πrh, where r is the radius and h is the height.
Given that the radius (r) of the hollow cylinder is 15 cm and the height (h) is 20 cm, we can substitute these values into the formula:
Curved Surface Area = 2π(15)(20) = 600π cm²
2. The area of a circle can be calculated using the formula:
Circular Base Area = πr², where r is the radius.
Since the hollow cylinder has two circular bases, we need to calculate the total area by multiplying the area of one base by 2.
Circular Base Area = 2(π)(15²) = 450π cm²
3. Finally, to find the total surface area, we add the curved surface area and the areas of the two circular bases together:
Total Surface Area = Curved Surface Area + Circular Base Area
= 600π + 450π
= 1050π cm²
Thus, the total surface area of the hollow cylinder is 1050π square centimeters.