To find the surface area of the net diagram of the right circular cylinder, we need to consider the cylinder's surface area formula, which consists of the lateral surface area and the area of the two circular bases.
The surface area \(A\) of a right circular cylinder can be calculated using the formula:
\[ A = 2\pi r h + 2\pi r^2 \]
where:
- \( r \) = radius of the base of the cylinder
- \( h \) = height of the cylinder
Given that:
- The radius \( r \) of the circles (bases of the cylinder) is 10 inches, and
- The height \( h \) of the cylinder is 9 inches,
we can calculate the surface area as follows:
- Calculate the lateral surface area:
\[ \text{Lateral Surface Area} = 2\pi rh = 2 \times 3.14 \times 10 \times 9 \]
\[ = 2 \times 3.14 \times 90 = 565.2 \text{ square inches} \]
- Calculate the area of the two circular bases:
\[ \text{Area of One Base} = \pi r^2 = 3.14 \times 10^2 = 3.14 \times 100 = 314 \text{ square inches} \]
\[ \text{Area of Two Bases} = 2 \times 314 = 628 \text{ square inches} \]
- Combine both areas to find the total surface area:
\[ \text{Total Surface Area} = \text{Lateral Surface Area} + \text{Area of Two Bases} = 565.2 + 628 \]
\[ = 1193.2 \text{ square inches} \]
So, the surface area of the net diagram of the right circular cylinder is 1193.2 square inches.