Question

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Square pyramids A and B are similar. In pyramid​ A, each base edge is 20 cm. In pyramid​ B, each base edge is 5 cm and the volume is 25 cm.
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

Below in bold.

Explanation:

a) The volumes will be in the ratio of the cubes of the edges.

So volume of A / volume B = 20^3 / 5^3

Volume A / 25 = 8000/125

Volume a = (25* 8000) / 125

= 8000/ 5

= 1600 cm^3.

b) ratio of the surface area of A to surface area of B

= 20^2 : 5^2

= 400:25

= 16:1.

c. The volume of pyramid B is 25 cm*3 so it' height is 25 / area of its base = 25/5^2

= 1 cm.

Now its slant height = √(1^2 + (2.5)^2)

= √7.25

= 2.6926 cm

So surface area = 25 + 4 * 1/2 * 5 * 2.6926

= 51.926

= 51.93 cm^2 to nearest hundredth.

and the surface area of pyramid B = 51.926 * 16

= 830.82 cm^2 to nearest hundredth.