Question

find the surface area of this cylinder. use 3.14 for π. do not round your answer. 4 cm 9 cm area of a circle (a = pi r^{2}) what is the area of both circles? both circles: ? (cm^{2})

Explanation:

Step1: Identify the radius

The radius $r$ of the circular - base of the cylinder is $r = 4$ cm.

Step2: Calculate the area of one - circle

The formula for the area of a circle is $A=\pi r^{2}$. Substituting $r = 4$ cm and $\pi=3.14$, we get $A_1 = 3.14\times4^{2}=3.14\times16 = 50.24$ $cm^{2}$.

Step3: Calculate the area of both circles

Since there are two circular bases in a cylinder, the area of both circles $A_{circles}=2\times A_1$. So $A_{circles}=2\times50.24 = 100.48$ $cm^{2}$.

Step4: Calculate the lateral - surface area

The formula for the lateral - surface area of a cylinder is $A_{lateral}=2\pi r h$, where $h = 9$ cm and $r = 4$ cm. Substituting the values, we have $A_{lateral}=2\times3.14\times4\times9=226.08$ $cm^{2}$.

Step5: Calculate the total surface area

The total surface area of a cylinder $A_{total}=A_{circles}+A_{lateral}$. So $A_{total}=100.48 + 226.08=326.56$ $cm^{2}$.

Answer:

The area of both circles is $100.48$ $cm^{2}$ and the total surface area of the cylinder is $326.56$ $cm^{2}$.