Question

1. a right circular cylinder has a radius of 3 yards and a length of 10 yards, as shown. find the surface area of the right circular cylinder.

Explanation:

Step1: Calculate the area of the two circular bases

The formula for the area of a circle is \(A = \pi r^{2}\). For two bases, \(A_{bases}=2\pi r^{2}\). Given \(r = 3\) yards, then \(A_{bases}=2\pi\times(3)^{2}=2\pi\times9 = 18\pi\) square yards.

Step2: Calculate the lateral surface area

The formula for the lateral - surface area of a cylinder is \(A_{lateral}=2\pi r h\) (where \(h\) is the height or length of the cylinder). Given \(r = 3\) yards and \(h = 10\) yards, then \(A_{lateral}=2\pi\times3\times10=60\pi\) square yards.

Step3: Calculate the total surface area

The formula for the total surface area of a cylinder is \(A = A_{bases}+A_{lateral}\). Substitute the values of \(A_{bases}\) and \(A_{lateral}\): \(A=18\pi + 60\pi=(18 + 60)\pi=78\pi\). Using \(\pi\approx3.14\), we get \(A = 78\times3.14=244.92\) square yards.

Answer:

The surface area of the right - circular cylinder is \(244.92\) square yards.