A gemstone is cut in the shape of a triangular pyramid. The area of the base of the pyramid is 42 square millimeters. The

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height of the pyramid is 4 millimeters. What is the volume of the gemstone? (Recall the formula V = 3 Bh)

56 cubic millimeters

84 cubic millimeters

168 cubic millimeters

336 cubic millimeters

56 cubic millimeters

Step-by-step explanation:

According to the question,a gemstone was cut in the shape of a triangular pyramid. The area of the base of the pyramid is 42 square millimeters. The height of that very pyramid is 4 millimeters. What is the volume of the gemstone?

Recall that the volume of a triangular pyramid is 1/3 × A × H

Where A is the has area

H is the height of the pyramid

And since we were provided with the base area,we can proceed to finding the volume if this very gemstone.

1/3 × 42 × 4

= 168/3

= 56 cubic millimeters.

The above is the volume of the gemstone

there is only one way to arrange all the eight relative to each other because they are not distinct. we have

now there are nine places to place an (and not more than one in one place).   because we have four symbols, we need to choose four of these nine places to insert an . order does not matter because the are not distinct.

thus there are 1 · c(9,4) ways, or, if we calculate it,

thus there are 126 ways to form such "words."