Question

find the surface area of a cylinder with a base diameter of 10 yd and a height of 7 yd. use the value 3.14 for $pi$, and do not do any rounding. be sure to include the correct unit.

Explanation:

Step1: Calculate the radius

The diameter $d = 10$ yd, so the radius $r=\frac{d}{2}=\frac{10}{2}=5$ yd.

Step2: Calculate the area of the two bases

The area of a single - base of a cylinder is $A_{base}=\pi r^{2}$. For two bases, $A_{2bases}=2\pi r^{2}$. Substituting $r = 5$ yd and $\pi=3.14$, we get $A_{2bases}=2\times3.14\times5^{2}=2\times3.14\times25 = 157$ yd².

Step3: Calculate the lateral surface area

The lateral - surface area of a cylinder is $A_{lateral}=2\pi r h$. Substituting $r = 5$ yd, $h = 7$ yd and $\pi = 3.14$, we have $A_{lateral}=2\times3.14\times5\times7=219.8$ yd².

Step4: Calculate the total surface area

The total surface area of a cylinder $A = A_{2bases}+A_{lateral}$. So $A=157 + 219.8=376.8$ yd².

Answer:

$376.8$ yd²