Answer:
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
