Question

Find the volume of the composite figure shown. Use 3.14 to approximate pi. Round your answer to the tenths.

Answer 1

Check the picture below.

so, the composite is really, a triangular prism on top of a rectangular prism with a semi-circle.

now, if we can just get the volume of each individual solid, then we're golden.

for the triangular prism, its volume is simply the triangular face's area times the length, in this case 20.

for the rectangular prism, is the same, the rectangular face's area times the length.

now, for the semicircle is the same, let's recall, the area of a full circle is πr², so the area of half a circle is (πr²)/2. Notice in the picture, the semi-circle has a radius of 11.

`\bf \stackrel{\textit{area of the triangle}}{\left[\cfrac{1}{2}(30)(15) \right]}(\stackrel{\textit{length}}{20})~~+~~ \stackrel{\textit{rectangle's area}}{(22\cdot 11)}(\stackrel{\textit{length}}{20})~~+ \stackrel{\textit{semi-circle's area}}{\left(\cfrac{\pi 11^2}{2} \right)}(\stackrel{\textit{length}}{20}) \\\\\\ 4500+4840+1210\pi \implies \stackrel{\pi =3.14}{13139.4}`

Answer 2

21499.4 in³

Explanation:

1. Find the area of the face:

a. Triangle: 1/2*b*h = 1/2*30*15 = 225 in²

b. Rectangle: b*h = 22*30 = 660 in²

c. Semi-circle: 1/2*πr² = 1/2*π*(d/2)² = 1/2*3.14*11² = 189.97 in²

d. Total: 225 + 660 + 189.97 = 1074.97 in²

2. Find height: 20 in

3. Find volume: 1074.97*20 = 21499.4 in³