What is the total surface area formula for a cylinder?

What is the total surface area formula for a cylinder?

• A. Total Surface Area = πr² + πrh
• B. Total Surface Area = 2πr(h + r)
• C. Total Surface Area = 2πrh
• D. Total Surface Area = πd²

Answer: (B)

The total surface area formula for a cylinder takes into account both the curved surface area and the area of the two circular bases. The formula is derived by summing these areas. For a cylinder with radius \( r \) and height \( h \): 1. The area of one circular base is \( \pi r^2 \). Since there are two bases, you multiply this by 2, giving \( 2 \pi r^2 \). 2. The curved surface area, which wraps around the sides of the cylinder, can be thought of as a rectangle when unrolled. The width of this rectangle is the circumference of the base, which is \( 2\pi r \), and the height is \( h \). Thus, the curved surface area is \( 2\pi rh \). When you combine these areas, the total surface area of the cylinder becomes: - Total Surface Area = Area of both bases + Curved Surface Area - Total Surface Area = \( 2\pi r^2 + 2\pi rh \) - This can also be factored into the final formula: Total Surface Area = \( 2\pi r(h + r) \). This is why the second option is correct

The total surface area formula for a cylinder takes into account both the curved surface area and the area of the two circular bases. The formula is derived by summing these areas.

For a cylinder with radius ( r ) and height ( h ):

1. The area of one circular base is ( \pi r^2 ). Since there are two bases, you multiply this by 2, giving ( 2 \pi r^2 ).

2. The curved surface area, which wraps around the sides of the cylinder, can be thought of as a rectangle when unrolled. The width of this rectangle is the circumference of the base, which is ( 2\pi r ), and the height is ( h ). Thus, the curved surface area is ( 2\pi rh ).

When you combine these areas, the total surface area of the cylinder becomes:

• Total Surface Area = Area of both bases + Curved Surface Area

• Total Surface Area = ( 2\pi r^2 + 2\pi rh )

• This can also be factored into the final formula: Total Surface Area = ( 2\pi r(h + r) ).

This is why the second option is correct