Three solid shapes a, b and c are similar.
the surface area of shape a is 4 cm^2
the surface area of shape b is 25 cm^2
the ratio of the volume of shape b to the volume of shape c is 27 : 64
work out the ratio of the height of shape a to the height of shape c.
give you answer in its simplest form.

Step-by-step explanation:

step 1

Find the ratio of the height of shape A to the height of shape B

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z-----> the scale factor

x----> surface area shape A

y----> surface area shape B

so

substitute

therefore

the ratio of the height of shape A to the height of shape B is equal to

step 2

Find the ratio of the height of shape B to the height of shape C

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> the scale factor

x----> volume shape B

y----> volume shape C

so

substitute

therefore

the ratio of the height of shape B to the height of shape C is equal to

step 3

Find the ratio of the height of shape A to the height of shape C

we have

Multiply

so

1/3

step-by-step explanation:

to find this, you can divide 12 by 4 which is 3 or you can multiply 4 until you reach 12 (4x3=12). both should give you 3, meaning theres three times less bananas than there are oranges.