Respuesta :
Answer:
Volume of tank = 461,814 ft³
Step-by-step explanation:
Congruent tanks implies that both tanks are of identifical shape, form & dimensions. Congruent means that the tanks have the same radius as well as height. Hence, the heights and radii of tanks #1 and #2 are equal and the same.
Let's list out the information given us:
radius(tank #1) = 35 ft ⇒ radius(tank #2) = 35 ft, height(tank #2) = 120 ft ⇒ height(tank #2) = 120 ft
Volume of cylinder = πr²h
The tanks have been cut into half, as such:
Volume of tank = ½πr²h
Volume of tank = Volume(tank #1) + Volume(tank #2)
Since the tanks are congruent (same dimensions), we have:
⇒ ½πr²h + ½πr²h ⇒ πr²h
Volume of tank = π * 35² * 120 = 147,000 π
Volume of tank = 461,814 ft³
The two holding tanks can be taken as one tank split halfway into two.
- The volume of both tanks combined, is approximately 461814.12 cubic feet.
Reasons:
Known parameters:
The given parameters are;
The shape of the bottom = A curve
Number of holding tanks = 2
The characteristics of the tanks = Congruent tanks
Dimension of tank #1 = Dimension of tank #2
The shape of each tank = Half cylinder
Radius of tank #1, r = 35 feet
Height of tank #2, h = 120 feet
Solution:
Given that the tanks are congruent and that each tank is a half cylinder, we have;
Sum of the volume of the tanks = Volume of tank having the radius of one of the tanks and the height of the other tank.
Sum of the volume of the tanks, V = π·r²·h
∴ V = π × 35² × 120 = 147,000·π ≈ 461814.12
The volume of both tanks, V ≈ 461814.12 ft.³
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