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(i) Take the (area of sector - area of triangle), then multiply by the length 10m, to find the volume

(ii) using CAH, and half the angle, express the height of the right-angled triangle as x. So, h is just the radius 0.2m, minus x.

(iii) First, find dv/d0 and dh/d0.

Sub h= 0.1m into the equation in part ii to find the value of ditter.

with the value of ditter, sub into dv/d0 to find its value, and dh/d0, separately. then using two equations as shown on the bottom left, find d0/dt using dV/dt and dv/d0. then sub d0/dt into the other equation to solve for dh/dt.

(iv) Find the capacity of the gutter simply by using area of semicircle x length of gutter. then divide by the rate of volume of water (0.015 - 0.005) = 0.01 to find the time taken for it to oveflow.

(ii) using CAH, and half the angle, express the height of the right-angled triangle as x. So, h is just the radius 0.2m, minus x.

(iii) First, find dv/d0 and dh/d0.

Sub h= 0.1m into the equation in part ii to find the value of ditter.

with the value of ditter, sub into dv/d0 to find its value, and dh/d0, separately. then using two equations as shown on the bottom left, find d0/dt using dV/dt and dv/d0. then sub d0/dt into the other equation to solve for dh/dt.

(iv) Find the capacity of the gutter simply by using area of semicircle x length of gutter. then divide by the rate of volume of water (0.015 - 0.005) = 0.01 to find the time taken for it to oveflow.

Date Posted:
2 years ago

dv/d0 should be 0.3 instead of 0.1, I think u made a mistake there.