To find the surface area of a cylinder, you can use the formula:
\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \]
where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder.
From your question, it looks like you might be providing dimensions in the form \( 2y , d \) and \( 3y , d \). I will assume:
- The diameter of the base of the cylinder is \( 2y , d \), which means the radius \( r \) is \( y , d \).
- The height \( h \) of the cylinder is \( 3y , d \).
Now, substituting in the values:
- \( r = y , d \)
- \( h = 3y , d \)
Now substitute these into the surface area formula:
\[ \text{Surface Area} = 2\pi (y , d)^2 + 2\pi (y , d)(3y , d) \]
Calculating each term:
-
Calculate \( 2\pi (y , d)^2 \): \[ 2\pi (y , d)^2 = 2\pi y^2 d^2 \]
-
Calculate \( 2\pi (y , d)(3y , d) \): \[ 2\pi (y , d)(3y , d) = 6\pi y^2 d^2 \]
Combine these together:
\[ \text{Surface Area} = 2\pi y^2 d^2 + 6\pi y^2 d^2 = 8\pi y^2 d^2 \]
Now substitute \( \pi \) with \( 3.14 \):
\[ \text{Surface Area} = 8 \times 3.14 \times y^2 d^2 \]
Calculating \( 8 \times 3.14 \):
\[ 8 \times 3.14 = 25.12 \]
Thus, the surface area is:
\[ \text{Surface Area} = 25.12 y^2 d^2 \]
So, the surface area of the cylinder is \( 25.12 y^2 d^2 \).