The sum of two numbers is 51. the difference of the numbers is 13. find the numbers
2 answers:
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*See attachment for the simplified model of the monument
Answer:
The correct option is B. 13ft.
YES to option B. NO to A and C.
Step-by-step Explanation:
=>Given: Model of the monument consisting of a rectangular pyramid and a rectangular prism having a total volume of 66ft³.
Volume of monument = Volume of Pyramid + Volume of Prism = 66ft³
=>Dimensions of given rectangular pyramid:
base length (l) = 3ft
base width = 2ft
height of pyramid (h) = ? (h = Unknown)
Base Area (B) = l × w = 3 × 2 = 6ft²
Volume of pyramid = ⅓ × base area (B) × h = ⅓ × 6 × h
V of Pyramid = 2h ft³
=> Dimensions of the rectangular prism:
base length (l) = 3ft
base width (w) = 2ft
Height of prism (h) = 10ft
Base area (B) = l × w = 3 × 2 = 6 ft³
Volume of prism = base area (B) × height (h)
V of prism = 6 × 10 = 60 ft³
We are required to find the possible height of the monument.
Height of monument = height of pyramid + height of prism
Height of pyramid is unknown (h)
Height of prism = 10ft
Let's find the height of the pyramid using the Volume of the monument = volume of pyramid + volume of prism
Thus,
V of monument = 66 ft³
V of pyramid = 2h ft³
V of prism = 60 ft³
Therefore,
66 = 2h + 60
Subtract 60 from both sides
66 - 60 = 2h + 60 - 60
6 = 2h
Divide both sides by 2
3 = h
Height of pyramid (h) = 3ft
Height of monument = h of Pyramid + h of prism
Height of monument = 3 + 10
Height of monument = 13ft.
The correct option is B. 13ft.
YES to option B. NO to A and C.
