(Solved): A container in the form of a right circular cone (vertex down) has radius \( a=11 \mathrm{~m} \) an ...

A container in the form of a right circular cone (vertex down) has radius \( a=11 \mathrm{~m} \) and height \( b=28 \mathrm{~m} \). (See the figure.) If water is poured into the container at a constant rate of \( 24 \mathrm{~m}^{3} / \mathrm{min} \), how fast is the water level rising when the water is I \( \mathrm{m} \) deep? Hint: The volume \( V \) of a cone of radius \( r \) and height \( h \) is \( V=\frac{1}{3} \pi r^{2} h \). The height of the cone and the radius ean be related using similar triangles. (Use decimal notation. Give your imswer to three decimal places.) \( \frac{d h}{d t} \) \( \mathrm{n} / \mathrm{min} \) A light in a lighthouse \( 1900 \mathrm{~m} \) from a straight shoreline is rotating at 2 revolutions per minute. How fast is the beam moving along the shore when it passes a point of \( 900 \mathrm{~m} \) from the point on the shore opposite the lighthouse? Hint: One revolution \( =2 \pi \mathrm{rad} \). (Give your answers as a whole number or exact number.) \( \frac{d}{d} \)