Question

1. find the surface area of the cylinder below.

39 cm
24 cm
9567.45 cm²
9556.27 cm²
9600.46 cm²
9500.17 cm²

Explanation:

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

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

Step2: Identify the given values

From the diagram, the radius \( r = 24\space cm \) and the height \( h=39\space cm \).

Step3: Calculate the area of the two circular bases

The area of one circular base is \( \pi r^2 \), so for two bases, it is \( 2\pi r^2 \). Substituting \( r = 24 \):

$$ 2\pi(24)^2=2\pi\times576 = 1152\pi $$

Step4: Calculate the lateral (curved) surface area

The lateral surface area is \( 2\pi rh \). Substituting \( r = 24 \) and \( h = 39 \):

$$ 2\pi\times24\times39=2\pi\times936 = 1872\pi $$

Step5: Calculate the total surface area

Add the area of the two bases and the lateral surface area:

$$ SA=1152\pi + 1872\pi=3024\pi $$

Now, calculate the numerical value using \( \pi\approx3.14159 \):

$$ SA = 3024\times3.14159\approx3024\times3.14159 $$

First, calculate \( 3000\times3.14159 = 9424.77 \) and \( 24\times3.14159=75.39816 \)
Then, add them together: \( 9424.77+75.39816 = 9500.16816\approx9500.17\space cm^2 \)

Answer:

\( 9500.17\space cm^2 \) (the last option)