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19 July, 02:31

P and Q are two geometrically similar solid shapes.

The total surface area of shape P is 720 cm².

The total surface area of shape Q is 2880 cm².

The volume of shape P is 3200 cmº.

Calculate the volume of shape Q.

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Answers (1)
  1. 19 July, 02:56
    0
    25600cm³

    Step-by-step explanation:

    We are given these values from the question

    The total surface area of shape P is 720 cm².

    The total surface area of shape Q is 2880 cm².

    The volume of shape P is 3200 cm³

    Step 1

    Find the scale factor of P to Q in terms of Length, Area and volume

    Using the surface area value:

    a. Scale factor for length

    2880 cm² : 720 cm²

    Divide through by 180

    = 16 : 4 = 16/4

    b. Scale factor for area

    √ 16/4=> 4/2

    c. Scale factor for volume

    (4/2) ³

    = 64/8

    In order to determine the Volume of shape Q, we would multiply the scale factor of the volume by the volume of P

    Volume of P = 3200 cm³

    Volume of Q =

    3200 cm³ * (64/8)

    = 25600cm³
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