McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
4. Volumes of Prisms and Cylinders
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Exercise 23 Page 835

Use the formula for the volume of a prism.

About 3935.4 cubic centimeters

Practice makes perfect

Let's analyze the given net.

After gluing together the appropriate sides of the same lengths, we get the following triangular prism.

We are asked to find the volume of the solid. We will use the formula for the volume of a prism. V=Bh Here, B represents the area of the base and h represents the height of the prism. This tells us that h=20 cm. The base is a right triangle with a hypotenuse of 31.4 cm and one leg that is 14 cm. Let x represent the second leg of the base.

Now, let's use the Pythagorean Theorem to find x.
x^2+14^2=31.4^2
Solve for x
x^2+196=985.96
x^2=789.96
x=sqrt(789.96)
x=28.1062270...
x≈ 28.11
Since the triangle base is a right triangle with legs that are 14 and 28.11 cm, its area is a half of the product of its legs. This tells us that B= 12* 14* 28.11=196.77 square centimeters. Now, let's substitute the values into the formula for volume.
V=Bh
V=( 196.77)( 20)
V=3935.4
Finally, we find that the volume of the solid is about 3935.4 cubic centimeters.