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.
What formula can be applied between
(a) SA = 2pie*r*h + 2pie*r^2
(b)SA = 2pie*r*h
State the reason why you choose (a) or (b).
not (a) since the ends are not included
not (b) since there is an inside and an outside
and it's pi not "pie"
As = 2*(pi*r^2) + 2pi*r*h.
My choice is "a" , because it includes the area of the circular ends and the
area due to the ht. of the cylinder.
To solve this question, we need to calculate the total surface area of a hollow cylinder. We have two formulas to choose from:
(a) SA = 2 * π * r * h + 2 * π * r^2
(b) SA = 2 * π * r * h
To determine which formula to apply, let's understand the parts of the formula and how they relate to the properties of the hollow cylinder.
- SA represents the total surface area of the hollow cylinder.
- π is a mathematical constant, approximately equal to 3.14159.
- r refers to the radius of the cylinder.
- h represents the height of the cylinder.
In the problem, the hollow cylinder's radius is given as 15 cm, and the height is given as 20 cm.
Formula (a) includes two terms: 2 * π * r * h and 2 * π * r^2. The first term accounts for the curved part of the cylinder (the lateral surface area), while the second term calculates the surface area of the two circular bases.
Formula (b) only includes one term: 2 * π * r * h, which represents the lateral surface area of the cylinder.
Since the problem specifies that the cylinder is hollow, it implies that the bases are removed or nonexistent. Therefore, we should not consider the surface area of the bases when calculating the total surface area. Consequently, we should choose formula (b) to find the surface area.
Now let's calculate the total surface area using formula (b):
SA = 2 * π * r * h
SA = 2 * π * 15 cm * 20 cm
SA = 600 cm^2 * π (approximate value)
Therefore, the total surface area of the hollow cylinder is 600π square centimeters.