Question

what is the surface area of this cylinder? round your answer to the nearest hundredth. 4.7 mm 10 mm square millimeters

Explanation:

Step1: Calculate area of two bases

The formula for the area of a circle is $A = \pi r^{2}$. The radius $r = 4.7$ mm. The area of two - bases is $2\times\pi r^{2}=2\times\pi\times(4.7)^{2}=2\times\pi\times22.09\approx 2\times3.14\times22.09 = 138.7112$ $mm^{2}$.

Step2: Calculate lateral surface area

The formula for the lateral - surface area of a cylinder is $A_{l}=2\pi rh$. Here, $r = 4.7$ mm and $h = 10$ mm. So $A_{l}=2\times\pi\times4.7\times10=94\pi\approx94\times3.14 = 295.16$ $mm^{2}$.

Step3: Calculate total surface area

The total surface area $A_{total}$ of a cylinder is the sum of the area of the two bases and the lateral - surface area. So $A_{total}=138.7112 + 295.16=433.8712\approx433.87$ $mm^{2}$.

Answer:

433.87