Big Ideas Math: Modeling Real Life, Grade 7
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Big Ideas Math: Modeling Real Life, Grade 7 View details
5. Volumes of Pyramids
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Exercise 4 Page 435

The volume of a pyramid is one third the area of its base times the height of the pyramid.

231cm^3

Practice makes perfect

Let's consider the given pyramid.

Triangular pyramid
We want to find the volume of the pyramid. Recall that the volume V of a pyramid is one third the area of the base B times the height of the pyramid h.

V=1/3 B h Let's use the diagram to identify the pyramid's height and write an expression for the area of its base. Remember that the area of a triangle is half the product of any base and its height.

Triangular pyramid
Now we can substitute 12* 7* 18 for B and 11 for h into the formula and calculate the volume of the pyramid.
V = 1/3Bh
V = 1/3 ( 1/2 * 7 * 18) (11)
V = (1/3 * 1/2) (7 * 18 * 11)
V = (1* 1/3* 2 ) (7 * 18 * 11)
V = (1/6 ) (1386)
V=1386/6
V= 231
The volume of the pyramid is 231 cubic centimeters.