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

square pyramid

step-by-step explanation:

square prism looks like nothing like that

triangular prism has a rectangular base instead of a square base

tetrahedron has a triangular base

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204