Question

What is the surface area of this composite solid?______________ square feet 242 319 363 517

Answer 1

Answer: I think the answer is 242or a

Step-by-step explanation:

Answer 2

Answer:

The right answer is 415.4 cubic feet.

Step-by-step explanation:

As you can observe in the image attached, the composite figure is formed by a square prism and a pyramid on top.

We need to find the volum of each part separately.

Square prism.

$V_{prims}=11 \times 11 \times 2=242 \ ft^{3}$

Square pyramid.

First, we need to find the height of the pyramid. We already know the height of each triangular face of the pyramid, which divides equally the side.

Let's use Pythagorean's Theorem to find the height of the pyramid.

$7^{2}=h^{2} +(5.5)^{2}\\ 49-30.25=h^{2}\\ h=\sqrt{18.75} \approx 4.3$

The height is 4.3 feet, approximately.

Now, we find the volume of the pyramid

$V_{pyramid}=\frac{1}{3}(11 \times 11 \times 4.3) \approx 173.4ft^{3}$

The sum of both figures represents the total volume of the composite figure

$V_{total}=242+173.4=415.4ft^{3}$

Therefore, the right answer is 415.4 cubic feet.