Two similar pyramids A and B have surface areas of 135cm^2 and 60cm^2. Volume of pyramid A is 405cm^3. Work out the volume of pyramid B

The area of pyramid B is 120cm³

Step-by-step explanation:

Since the shapes are similar, then one is an enlargement of the other using a scale factor. To find the scale factor we have to take the quotient of the surface areas then take the square root. We are looking for the scale factor because we will use it to find the volume of pyramid B.

scale factor = √(60/135) = √(4/9) = 2/3, 2 and 3 correspond to pyramids B and A respectively.

We took the square root because area factor = (scale factor)². By taking the quotient, the area factor is gotten. Therefore to get the scale factor we need to take the square root of the area factor.

Volume factor = (scale factor)³

Volume factor = (2/3)³ = 8/27

8/27 = x/405

x = (8 * 405)/27 = 8 * 15 = 120.

Therefore the area of pyramid B is 120cm³.