Question

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

Answer 1

Answer:

the ratio of the surface area of Pyramid A to Pyramid B is: $\frac{36}{49}$

Step-by-step 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.

<=> $\frac{Volume of A }{Volume of B}$ =$(\frac{a}{b}) ^{3}$ =  $\frac{684}{1029}$ = $\frac{216}{343}$

<=> $\frac{a}{b} =$$\frac{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

<=> $\frac{surface area of A}{surface area of B} =( \frac{a}{b}) ^{2}$

= $\frac{36}{49}$

So  the ratio of the surface area of Pyramid A to Pyramid B is: $\frac{36}{49}$