Pyramid A is a right square pyramid with a height of 133m and a square base with a perimeter of 492m. Pyramid B has a square base with a per

Question

Pyramid A is a right square pyramid with a height of 133m and a square base with a perimeter of 492m. Pyramid B has a square base with a perimeter of 592m and a height of 247m. Which pyramid has the greater volume and by how many times as​ great?

in progress 0
Thu Giang 3 years 2021-07-16T19:56:01+00:00 1 Answers 20 views 0

Answers ( )

  1. Acacia
    0
    2021-07-16T19:57:36+00:00
    Reply

    9514 1404 393

    Answer:

      Pyramid B is 2.6888 times the volume of pyramid A

    Step-by-step explanation:

    The volume is proportional to the height, and to the square of the linear measure of the base.

    Then the ratio of volumes will be …

      B/A = (592²·247)/(492²·133) = 86564608/32194512 ≈ 2.6888

    Pyramid B has the greater volume by a factor of about 2.6888.

    _____

    Additional comment

    The actual volumes in cubic meters will be 1/48 of the numbers we used in the ratio above.

    If you recall that the side length is related to the perimeter by …

      P = 4s   ⇒   s = P/4

    and the volume is …

      V = 1/3s²h

    Then you have …

      V = 1/3(P/4)²h = 1/48·P²h . . . . . . P²h is the number we used above

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )