Three solid shapes A, B and C are similar - Edexcel - GCSE Maths - Question 16 - 2018 - Paper 1

Given the volume ratio of shape B to shape C as 27:64, we can derive the ratio of lengths. The volume ratio is proportional to the cube of the ratio of corresponding lengths. If the ratio of lengths is ( m ), we have:

$\frac{Volume \ of \ B}{Volume \ of \ C} = \frac{27}{64} = m^3$

Thus, solving for m gives:

$m = \sqrt[3]{\frac{27}{64}} = \frac{3}{4}$

Finally, the ratio of the height of shape A to the height of shape C can be derived by using the ratios we found. We know:

• The ratio of lengths A to B is ( \frac{2}{5} )
• The ratio of lengths B to C is ( \frac{3}{4} )

To find the ratio A to C, we multiply the ratios:

$\frac{Height \ of \ A}{Height \ of \ C} = \frac{Height \ of \ A}{Height \ of \ B} \times \frac{Height \ of \ B}{Height \ of \ C} = \frac{2}{5} \times \frac{3}{4} = \frac{6}{20} = \frac{3}{10}$

Thus, the ratio of the height of shape A to the height of shape C is ( \frac{3}{10} ).