Answered

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:

a) Work 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.



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.