Answer:
A
Step-by-step explanation:
We can see that our figure is composed of a cylinder and a cone.
So, we can utilize the surface area formulas.
The surface area of a cylinder is given by:
[tex]SA=2\pi r^2+2\pi r h[/tex]
The first term is the two circular bases, and the second term is the lateral surface area.
Notice that the circular base has a diameter of 6. So, its radius is 3.
Also, the height of the cylinder is 50.
However, notice that one of the circular bases is not included in our surface area as it’s connected to the cone. So, we will remove that from our surface area. This gives us:
[tex]SA=\pi r^2+2\pi rh[/tex]
Therefore, by substituting 3 for r, the radius, and 50 for the height h we can see that:
[tex]\begin{aligned}SA&=\pi(3)^2+2\pi(3)(50)\\&=9\pi+300\pi\\&=309\pi\end{aligned}[/tex]
Now, we can determine the SA of the cone.
Again, we will only need to lateral surface area, since the circular base is connected to the cylinder.
The lateral surface area of a cone is given by the formula:
[tex]SA=\pi r\ell[/tex]
Where r is the radius and l is the slant height.
The radius is 3 and the slant height is 5. Therefore:
[tex]SA=\pi(3)(5)=15\pi[/tex]
So, our total surface area is:
[tex]SA_{\text{Total}}=309\pi+15\pi[/tex]
Simplify:
[tex]SA_{\text{Total}}=324\pi\\[/tex]
Approximate:
[tex]SA_{\text{Total}}\approx1017.9\text{ units}^2[/tex]
Hence, our answer is A.
