Math, asked by sarathkumarmarri135, 29 days ago

Q 56. Consider a water tank filling at a rate of Q cubic metres per minute. The structure of tank has a cube of side L at its base, and a cylinder kept on the cube such that the flat circular part of cylinder touches the four edges of one face of the cube. The height of cylinder is h. What is the rate of change of height from the ground if the water surface is in cylinder now? Ops: A. O 2Q / (na?) B. O4Q/ (na? C. O 20/ (n ah) D. O4Q/ (nah)

Answers

Answered by RvChaudharY50

Given :- Consider a water tank filling at a rate of Q cubic metres per minute. The structure of tank has a cube of side L at its base, and a cylinder kept on the cube such that the flat circular part of cylinder touches the four edges of one face of the cube. The height of cylinder is h.

To Find :- What is the rate of change of height from the ground if the water surface is in cylinder now ?

Solution :-

we have,

→ Filling rate of water tank = Q m³ / min .

→ Side of base of cube = L m .

since, cylinder kept on the cube such that the flat circular part of cylinder touches the four edges of one face of the cube .

so,

→ Radius of cylinder = Side of cube / 2 = (L/2) m .

then,

→ Base area of cylinder * Rate of change of height = Filling rate of water tank

→ πr² * Rate of change of height = Q

→ π(L/2)² * Rate of change of height = Q

→ π * (L²/4) * Rate of change of height = Q

→ Rate of change of height = Q * 4 / π * L²

→ Rate of change of height = (4Q/πL²)

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Answered by amitnrw

Given : a water tank filling at a rate of Q cubic metres per minute

The structure of tank has a cube of side L at its base, and a cylinder kept on the cube such that the flat circular part of cylinder touches the four edges of one face of the cube.

The height of cylinder is h.

To Find : What is the rate of change of height from the ground

Solution:

a cylinder kept on the cube such that the flat circular part of cylinder touches the four edges of one face of the cube.

Hence Diameter of cylinder = L

=> Radius = L/2

height of cylinder is h.

Volume of cylinder V = π (L/2)² h = πL²h/4

V = πL²h/4

dV/dt = ( πL²/4) dh/dt

dV/dt = Q m³ / min

( πL²/4) dh/dt = Q