Question

Worth 23 Points!!! PLEASE HELP. Square pyramids A and B are similar. In pyramid​ A, each base edge is 10 cm. In pyramid​ B, each base edge is 5 cm and the volume is 50 cm cubed.
a. Find the volume of pyramid A.

b. Find the ratio of the surface area of A to the surface area of B.

c. Find the surface area of each pyramid.

Answer 1

Answer:

a) 400

b) 4

c) 90 for pyramid A, 360 for pyramid B

Step-by-step explanation:

Since the two triangles are similar, if one of the dimensions of the triangles is twice that of the other, than all of the other dimensions are as well. Since a pyramid is a 3D shape, and there are three dimensions, it has a volume of $2^3=8$ times greater, which is equal to 50*8=400 cubic centimeters. Since the surface area is a 2D object, the one of pyramid A is only $2^2=4$ times as large. Now, to find the surface area of both pyramids, you first need to find their height. However, you can do this by reversing the formula for the volume of a pyramid, which is $V=\frac{1}{3}s^2$. Plugging in our known numbers, you get:

$50=\frac{1}{3}\cdot 5^2\cdot h$

$150=25h$

$h=6$

From this, you can find the surface area of pyramid B with the formula $a^2+2a\sqrt{\frac{a^2}{4}+h^2}=25+10\sqrt{\frac{25}{4}+36}=25+10\cdot \frac{13}{2}=25+65=90$. Multiplying this by 4 to get the surface area of pyramid A, you get 360 square centimeters. Hope this helps!