Question

find the surface area of this cylinder. use 3.14 for π. do not round your answer. 30 cm = diameter 40 cm what is the area of both circles? both circles: ?cm² rectangle: cm² total sa: cm² area of a circle a = πr²

Explanation:

Step1: Calculate the radius

Given diameter $d = 30$ cm, radius $r=\frac{d}{2}=\frac{30}{2}=15$ cm.

Step2: Find the area of one - circle

The area of a circle formula is $a = \pi r^{2}$. Substituting $\pi = 3.14$ and $r = 15$ cm, we get $a=3.14\times15^{2}=3.14\times225 = 706.5$ $cm^{2}$.

Step3: Calculate the area of both circles

Since there are two circular bases, the area of both circles is $2\times a=2\times706.5 = 1413$ $cm^{2}$.

Step4: Calculate the lateral - surface area

The lateral - surface area of a cylinder is $A_{l}=2\pi r h$. Here, $h = 40$ cm, $r = 15$ cm, and $\pi=3.14$. So $A_{l}=2\times3.14\times15\times40=3768$ $cm^{2}$.

Step5: Calculate the total surface area

The total surface area of a cylinder $SA=2\pi r^{2}+2\pi r h$. Substituting the values of the area of two circles and the lateral - surface area, we get $SA = 1413+3768=5181$ $cm^{2}$.

Answer:

The area of both circles is $1413$ $cm^{2}$, the area of the rectangle (lateral - surface area) is $3768$ $cm^{2}$, and the total surface area is $5181$ $cm^{2}$.