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Jing Yi is sculpting a small pyramid as a model for a larger pyramid that will be used as a stage prop. The model pyramid has a square base that measures 15 cm on each side. The pyramid has a height of 12 cm.
3a. How much plaster does she need to make the smaller scale model? Show your work, and include the units in your answer. (2 points)

3b. The actual stage prop will have a base that is 3 times as long and 3 times as wide, and it will stand 3 times taller. How much plaster does she need to make the actual stage prop? Show your work, and include the units in your answer. (2 points)
Answer:


3c. How many times the volume does the actual stage prop have than the scale model? (Hint: either divide the volume of the actual prop by the volume of the scale model, or apply the relevant theorem.) (1 points)
Answer:


Respuesta :

Ashraf82

Answer:

3a. ⇒ 2700 cm³

3b. ⇒ 72,900 cm³

3c. ⇒ 27

Step-by-step explanation:

3a.

∵ The model in a shape of square pyramid

∴ Its volume = base area × height

∵ Base shaped square with side length 15 cm

∴ Area of base = 15 × 15 = 225 cm²

∵ The model height = 12 cm

∴ She needs = 225 × 12 = 2,700 cm³ of plaster

3b.

∵ Each dimension in the actual stage = 3 times the model

∴ The side of the square base = 15 × 3 = 45 cm

∴ The height = 12 × 3 = 36 cm

∴ The area of the base = 45 × 45 = 2,025 cm²

∴ She needs = 2025 × 36 = 72,900 cm³ of plaster

3c.

∵ Each length in the actual stage is 3 times the model

∴ The volume of the actual stage = (3)³ the volume of the model

∴ The volume of the actual stage = 27 the volume of the model

To check your answer:

Volume actual ÷ Volume model = 72,900 ÷ 2700 = 27

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