Question

12 a can in the shape of a cylinder has a diameter of 6 centimeters and a height of 10 centimeters. which measurement is closest to the total surface area of the can in square centimeters? f 603.19 cm² g 245.04 cm² h 376.99 cm² j 188.50 cm²

Explanation:

Step1: Recall the formula for the total surface area of a cylinder

The total surface area \( SA \) of a cylinder is given by the formula \( SA = 2\pi r^2 + 2\pi rh \), where \( r \) is the radius and \( h \) is the height.

Step2: Find the radius

The diameter \( d = 6 \) cm, so the radius \( r=\frac{d}{2}=\frac{6}{2} = 3 \) cm. The height \( h = 10 \) cm.

Step3: Calculate the two parts of the surface area

First, calculate the area of the two circular bases: \( 2\pi r^2=2\times\pi\times3^2 = 2\times\pi\times9=18\pi \).
Then, calculate the lateral (curved) surface area: \( 2\pi rh = 2\times\pi\times3\times10 = 60\pi \).

Step4: Sum the two parts to get the total surface area

\( SA=18\pi + 60\pi=78\pi \). Now, substitute \( \pi\approx3.1416 \): \( SA\approx78\times3.1416 = 245.0448 \approx 245.04 \) \( cm^2 \).

Answer:

G \( 245.04 \space cm^2 \)