A pyramid has a base 16 inches x 16 inches and a slant height of 10 inches. what is the volume in cubic inches

Mathematics

1 answer:

gizmo_the_mogwai [7]4 years ago

4 0

Answer:

512 in³

Step-by-step explanation:

The height perpendicular to the base is the leg of a right triangle with hypotenuse 10 in and other leg 8 in. Using the Pythagorean theorem, we can find it as ...

h² +8² = 10²

h² = 100 -64 . . . . . subtract 8²

h = 6 . . . . . . . . . . . . take the square root of 36

Then the volume is found using ...

V = (1/3)Bh = (1/3)(16 in)²(6 in) = 512 in³

The volume is 512 cubic inches.

_____

The 8-inch dimension used above comes from half the distance between the center of one side of the base to the center of the opposite side. (16 in)/2 = 8 in.

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