Similar Solids Help

[knpoe03]

Hello there! This is my first time posting, so I apologize if I make any mistakes. My teacher is unavailable to answer my questions thanks to COVID-19, but I'd appreciate any help that you have to offer.

I keep messing up these two problems.

1) The ratio of the volume of 2 similar solids is 64:729. If the surface area of the larger solid is 567 square kilometers, what is the surface area of the smaller solid? (My answer was 168, but for some reason I'm wrong.)

2) Pyramid A and Pyramid B are similar. The volume of Pyramid A is 448 cubic inches and the volume of Pyramid B is 189 cubic inches. If the height of Pyramid B is 39 inches, what is the height of Pyramid A? (My answer was 92, but I was also wrong here.)

Any help or corrections to my mistakes would be helpful! Thanks!

 

[MarkFL]

Hello, and welcome to FMH!

If two solids are similar, then the ratio of corresponding surface areas will vary as the square of the ratio of corresponding linear measures. The ratio of their volumes will vary as the cube of the ratio of corresponding linear measures.

In the first problem we are told:

[MATH]\frac{V_L}{V_S}=\frac{729}{64}=\left(\frac{9}{4}\right)^3[/MATH]
And so we must have:

[MATH]\frac{A_L}{A_S}=\left(\frac{9}{4}\right)^2[/MATH]
Can you proceed