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
<em>To check your answer:</em>
Volume actual ÷ Volume model = 72,900 ÷ 2700 = 27
