surface area of a cylinder with a radius of 4m and a height of 10m

asked by guest
on Mar 17, 2025 at 1:19 am



MathBot Answer:

The surface area of a cylinder is 112π351.86m2112 \pi \approx 351.86\, \text{m}^2.

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


Given: r=4h=10\begin{aligned}r&=4\\h&=10\end{aligned}

Surface area

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

Solution:S=2πr(r+h)S=2π(4)((4)+(10))S=112π\begin{aligned}S&=2 \pi r \left(r + h\right)\\S&=2 \pi \left(4\right) \left(\left(4\right) + \left(10\right)\right)\\S&=112 \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 PB, of a cylinder is the distance around the base.C=PB=2πr=πd\begin{aligned} C = P_{B} &= 2 \pi r \\ &= \pi d \end{aligned}

The base area AB of a cylinder is the region enclosed inside the base. AB=πr2A_{B} = \pi r^{2}

The lateral surface area AL 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. AL=Ch=2πrh\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. S=2AB+AL=2πr(r+h)\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. V=ABh=πr2h\begin{aligned} V &= A_{B} h \\ &= \pi r^{2} h \end{aligned}