A jewelry store is featuring a diamond in the shape of a square pyramid. The side length of the diamond is 8 millimeters and the

Question

A jewelry store is featuring a diamond in the shape of a square pyramid. The side length of

the diamond is 8 millimeters and the slant height is 6 millimeters.

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Ngọc Diệp 4 years 2021-08-17T15:37:42+00:00 1 Answers 21 views 0

Answers ( )

  1. linhdan
    0
    2021-08-17T15:38:49+00:00
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    Answer:

    128√5/3 mm³

    Step-by-step explanation:

    Since we are not told what to find, we can as well look for the volume of the pyramid

    Volume of a square pyramid: V = (1/3)a²h

    a is the side length of the square

    h is the height of the pyramid

    Given

    a = 8mm

    l² = (a/2)² + h²

    l² = (a/2)² + h²

    6² = (8/2)² + h²

    h² = 6² – 4²

    h² = 36 – 16

    h² = 20

    h = √20

    Volume of a square pyramid =  (1/3)*8²*√20

    Volume of a square pyramid = 1/3 * 64 * 2√5

    Volume of a square pyramid = 128√5/3 mm³

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