The two triangular pyramids are similar. the smaller pyramid has a volume of 52 inches3. what is the volume of the larger pyramid? round to the nearest tenth. in.3

the volume of the larger pyramid = 175.5 inches³

Step-by-step explanation:

* Lets revise the similar

- If two solids are similar,then the ratio between each two

 corresponding dimensions are qual

- Their perimeters have the same ratio

- Their areas have the square of the equal ratio

- Their volumes have the cube of the equal ratio

* Lets solve the problem

- The two triangular pyramids are similar

- The perimeter of the base of the small one = 14 inches

- The perimeter of the base of the big one = 21 inches

∴ The ratio of the similarity = 14/21 = 2/3

∴ The ratio between their volumes is (2/3)³ = 8/27

∵ The volume of the small one = 52 inches³

- W will us the cub of the ratio to find the larger volume

∴ 52/V = 8/27 ⇒ by using the cross multiplication

∴ 52 × 27 = 8 × V

∴ 1404 = 8V ⇒ divide both sides by 8

∴ V = 175.5 inches³

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