Question

The ratio heights is?The ratio of the surface areas is? The ratio of the volumes is?

Answer 1

If the two solids are similar, then

The ratio between their corresponding dimensions is

`b_1:b_2=h_1:h_2`

The ratio between their surface areas is

`A_1:A_2=(b_1:b_2)^2`

The ratio between their volumes is

`V_1:V_2=(b_1:b_2)^3`

From the given figure we can see

The base length of the pyramid PQRST = 5 m

The base length of the pyramid JKLMN = 25 m

Then the ratio between their bases is

`(b_1)/(b_2)=(5)/(25)=(1)/(5)`

The ratio between their heights is

`(h_1)/(h_2)=(1)/(5)`

The ratio between their surface area is

`(A_1)/(A_2)=((1)/(5))^2=(1)/(25)`

The ratio between their volumes is

`(V_1)/(V_2)=((1)/(5))^3=(1)/(125)`

h(A): h(B) = 1: 5

S.A(A): S.A(B) = 1: 25

V(A): V(B) = 1: 125