Math Problem Solver

The surface area of a cylinder is $266 \pi \approx 835.66\, \text{cm}^2$.

Note: Approximate solutions are rounded to the nearest hundredths place.

Given: $$\begin{aligned}h&=12\\r&=7\end{aligned}$$

Surface area

The surface area of a cylinder is given by the equation: $$\begin{aligned}S&=2 \pi r \left(r + h\right)\end{aligned}$$ where $S$ is surface area, $r$ is radius, and $h$ is height.

Solution:$$\begin{aligned}S&=2 \pi r \left(r + h\right)\\S&=2 \pi \left(7\right) \left(\left(7\right) + \left(12\right)\right)\\S&=266 \pi\end{aligned}$$

A right cylinder is a three dimensional solid with two parallel, congrugent flat faces and one curved surface. The circular faces are the base and top of a cylinder. The radius r is the distance between the center of the base and any point on the circumference of the base. The diameter d is twice the radius, forming a line segment passing through the center of the base. The height h is the perpendicular distance between the base and the top.

The (base) circumference C, or base perimeter P_B, of a cylinder is the distance around the base.$$\begin{aligned} C = P_{B} &= 2 \pi r \\ &= \pi d \end{aligned}$$

The base area A_B of a cylinder is the region enclosed inside the base. $$A_{B} = \pi r^{2}$$

The lateral surface area A_L of a cylinder is the area of the curved surface, flattened to be a rectangle with the base being the circumference of a cylinder and the height being the height of a cylinder. $$\begin{aligned} A_{L} &= C h \\ &= 2 \pi r h \end{aligned}$$

The surface area S of a cylinder is the region occupied by its base, top, and curved surface. $$\begin{aligned} S &= 2 A_{B} + A_{L} \\ &= 2 \pi r (r + h) \end{aligned}$$

The volume V of a cylinder is the amount of space it occupies. $$\begin{aligned} V &= A_{B} h \\ &= \pi r^{2} h \end{aligned}$$