Question

Pyramid A and Pyramid B are similar. Pyramid A has a volume of 648 m and Pyramid B has a

volume of 1,029 m². What is the ratio of the surface area of Pyramid A to Pyramid B?​

Answer 1

the ratio of the surface area of Pyramid A to Pyramid B is:
`(36)/(49)`

Explanation:

Given the information:

• Pyramid A : 648
  `m^(3)`
• Pyramid B : 1,029
  `m^(3)`
• Pyramid A and Pyramid B are similar

As we know that:

If two solids are similar, then the ratio of their volumes is equal to the cube

of the ratio of their corresponding linear measures.

<=>
`(Volume of A )/(Volume of B)` =
`((a)/(b)) ^(3)` =
`(684)/(1029)` =
`(216)/(343)`

<=>
`(a)/(b) =`
`(6)/(7)`

Howver, If two solids are similar, then the n ratio of their surface areas is equal to the square of the ratio of their corresponding linear measures

<=>
`(surface area of A)/(surface area of B) =( (a)/(b)) ^(2)`

=
`(36)/(49)`

So the ratio of the surface area of Pyramid A to Pyramid B is:
`(36)/(49)`