Question
what is the formula for the total area of a cylinder
Answers
GPT-4o mini
The total surface area \( A \) of a cylinder can be calculated using the formula:
\[
A = 2\pi r(h + r)
\]
where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is a constant approximately equal to 3.14159.
This formula includes both the lateral surface area and the area of the two circular bases.
- The lateral surface area is given by \( 2\pi rh \).
- The area of the two bases combined is \( 2\pi r^2 \).
Thus, combining these gives the total surface area:
\[
A = 2\pi rh + 2\pi r^2 = 2\pi r(h + r)
\]
\[
A = 2\pi r(h + r)
\]
where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is a constant approximately equal to 3.14159.
This formula includes both the lateral surface area and the area of the two circular bases.
- The lateral surface area is given by \( 2\pi rh \).
- The area of the two bases combined is \( 2\pi r^2 \).
Thus, combining these gives the total surface area:
\[
A = 2\pi rh + 2\pi r^2 = 2\pi r(h + r)
\]