Question

find the surface area of the figure to the nearest tenth.

Explanation:

Step1: Calculate the lateral - area of the cone

The formula for the lateral area of a cone is $A_{l - cone}=\pi rl$, where $r = 4$ cm and $l = 8$ cm.
$A_{l - cone}=\pi\times4\times8=32\pi$ cm².

Step2: Calculate the lateral - area of the cylinder

The formula for the lateral area of a cylinder is $A_{l - cylinder}=2\pi rh$, where $r = 4$ cm and $h = 6$ cm.
$A_{l - cylinder}=2\pi\times4\times6 = 48\pi$ cm².

Step3: Calculate the area of the base of the cylinder

The formula for the area of a circle (base of the cylinder) is $A_{base}=\pi r^{2}$, where $r = 4$ cm.
$A_{base}=\pi\times4^{2}=16\pi$ cm².

Step4: Calculate the total surface area of the figure

The total surface area $A$ of the figure is the sum of the lateral area of the cone, the lateral area of the cylinder, and the area of the base of the cylinder.
$A=32\pi + 48\pi+16\pi=96\pi$ cm².
Now, substitute $\pi\approx3.14159$:
$A\approx96\times3.14159 = 301.6$ cm².

Answer:

$301.6$ cm²