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

$\frac{b_1}{b_2}=\frac{5}{25}=\frac{1}{5}$

The ratio between their heights is

$\frac{h_1}{h_2}=\frac{1}{5}$

The ratio between their surface area is

$\frac{A_1}{A_2}=(\frac{1}{5})^2=\frac{1}{25}$

The ratio between their volumes is

$\frac{V_1}{V_2}=(\frac{1}{5})^3=\frac{1}{125}$

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

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

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