A 24-centimeter tall vase has cross sections parallel to the base that are circles. Each circular cross section $h$ centimeters above the base has a radius of $r(h)=8-0.1 h+2 \sin \left(0.3 h^{0.9}\right)$ centimeters for $0 \leq h \leq 24$. A sketch of the vase and the graph of $r$ are shown above. (a) Find the area of the region between the graph of $r$ and the $h$-axis from $h=0$ to $h=24$. (b) Find the volume of the vase. (c) Evaluate $\int_{4}^{20} r^{\prime}(h) d h$. Using correct units, interpret the meaning of $\int_{4}^{20} r^{\prime}(h) d h$ in the context of the problem. (d) Water is poured into the vase. At the instant when the depth of the water in the vase is 10 centimeters, the depth of the water is increasing at a rate of 0.6 centimeter per second. At that instant, what is the rate of change of the circumference of the surface of the water, in centimeters per second?convince me pls

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