QCEVault

Applications of integral calculus — Question 208

Original QCE Vault practice · 8 marks

Q208 · Practice questionTechnology-freeComplex unfamiliar8 marks

QUESTION 208 (8 marks)

A vessel design starts with region R below y=xy=\sqrt x, above the x-axis and to the left of x=4. R is rotated about the y-axis.
Hatched region under y=sqrt(x), above the x-axis and left of x=4.
a)
Determine the exact solid volume.
[3 marks]
b)
What fraction of a radius-four, height-two cylinder does this solid occupy?
[2 marks]
c)
Interpret this same solid as the internal capacity of a vessel, with dimensions in centimetres. When filled to height h, its cross-section is the annulus with radii 4 and h2h^2. Liquid enters at 3π3\pi cm3^3/min. Determine dh/dtdh/dt when h=1 cm.
[3 marks]
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