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The volume of statue B is 20% less than the volume of statue A



The surface area of statue B is k% less than the surface area of statue A



You will need to work out the value of k by following the steps below:


AWork out the length scale factor from statue A to statue B. Give your answer correct to 3 decimal places but keep it in surd format on your calculator when using for further calculations.

Verified Answer :

  1. Volume Scale Factor:

    • The volume of statue B is 20% less than the volume of statue A.
    • Volume of B = 0.8 times Volume of A.

    2. Length Scale Factor:

    • The volume scale factor is the cube of the length scale factor.
    • k cubed equals 0.8.
    • k equals the cube root of 0.8, which is approximately 0.928.

    3. Surface Area Scale Factor:

    • The surface area scale factor is the square of the length scale factor.
    • Surface area scale factor equals (cube root of 0.8) squared, which is approximately 0.860.

    4. Percentage Reduction in Surface Area:

    • The surface area of statue B is the surface area scale factor times the surface area of statue A.
    • Surface Area of B equals 0.860 times Surface Area of A.
    • The percentage reduction k is calculated as:
    • k equals (1 minus 0.860) times 100 percent.
    • k equals 0.140 times 100 percent.
    • k equals 14 percent.

    So, the surface area of statue B is 14 percent less than the surface area of statue A.

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