Maths-
General
Easy
Question
A conical vessel of height 10ft and semivertical angle
is full of water. If empties in such away that the height at the water in the vessel is decreasing at a constant rate of 1ft/min. Then the rate at which the volume of water in the vessel is decreasing when its height is 6ft. is
Hint:
Rate of change of volume with respect to time (
) = ![1 third straight pi fraction numerator d over denominator d t end fraction left parenthesis r squared straight h right parenthesis](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFsAAAAjCAYAAAD7R3Y1AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAwpJREFUeNrtWk9kXEEcHlGrKkr0EFFVKqJyiKWHqIrKdfUQoYeeKkpERPXWU+ypRPQQ0WtVVZVVOUWFqqiIKFXVQ8Veeqheq6LWs5bXb+xX1njv7byZnTcvk/342B27OzPf/ub3Z95PiGxMgevgV1E+tMARERBegctgXLJ1TYLfRKAom9gL4Juh2IPHKLgN/gEj8C34DHw8FHuwkD55H1zi64tgnetZGIo9WKynWHATvDwUe7D4STeiWntLBAwfYlfBjwnjs3Qtrvcr2QYPmf0ELfYiU08V98AXBcaMVfBL6GLLANjIyP3zQoq2YbiWyOA7G5zzVIh9AfxOdyJxA9wFf4G1nL81Ax4ZruN2ijvTwSHnzuW7elkkxsEdWpYUax78DZ432HTVYP4JfveaofFJAzkQZwhVCpYXUzxJE5Yn/YCinwlsgmsGFv2ORZStW31oESsyMSa6N4SdFBfkwxXtgXMJ43UWTCvgZ7qq/wWUFPq6Rgyr0b1F9OtXEj57E/zgYmPyuDwBzyWIGnmy7BOwkjDeYLB9muKTswxEvn+g/ClLKYG0wjUUmi76EruTMt5kLm+6t9cJOXk75fNtncxDh7Zixw7YT2zbkj9OyYhiXbFdW3anRG7EtuSPc4wX4kY6JSiMJN6DtwZc8ucR21mA7D2mqttopQQqH6nfNgNcEWKvcQ3OcBX8q4zJFEneT0+XoKjZMSj5TcV2XtSsMr/tRY3WvenBuo+UOwqTkt9EbK1yfZ45ZIvuQKZJW+Alz9WgafuCzUWUDbQuovaZg1aU47jnUWi1fWEy553HiquyOSNWLNv8wIlHsdX2hcWEwiIYyJL2uKC5+rUv1JUiJpi2hnHW/U3LCJ4nbdRpX2iIgNoZ1BL4UUHz6rYvHDPFDApjtKBPovuIyDV02heCb2cYpeCuCxCd9oVZYf5c8NTA9TWpbvuCfP8yZKFn6Dddp3c67QtbIv+jrtJCHtG7ovvEZYQV5Q/wvuN5ddsXZBr4PBSx57jJiJT+8k6BqWa/9oVp/gGx8HOTaIR/BHcAqmIXn/QAAAEVdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtbj4xPC9tbj48bW4+MzwvbW4+PC9tZnJhYz48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+JiN4M0MwOzwvbWk+PG1mcmFjPjxtaT5kPC9taT48bXJvdz48bWk+ZDwvbWk+PG1pPnQ8L21pPjwvbXJvdz48L21mcmFjPjxtbz4oPC9tbz48bXN1cD48bWk+cjwvbWk+PG1uPjI8L21uPjwvbXN1cD48bWkgbWF0aHZhcmlhbnQ9Im5vcm1hbCI+aDwvbWk+PG1vPik8L21vPjwvbWF0aD7w91BHAAAAAElFTkSuQmCC)
The correct answer is: ![12 pi](data:image/png;base64,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)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/1718719/1/894543/Untitled.png?time=1662664279459)
Given :
![theta space equals space 30 degree
h space equals space 10 f t
fraction numerator d h over denominator d t end fraction space equals space 1 f t divided by m i n
r a t e space o f space c h a n g e space left parenthesis h right parenthesis space equals space 6 f t](data:image/png;base64,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)
We know that, tan
= ![fraction numerator o p p o s i t e space s i d e over denominator a d j a c e n t space s i d e end fraction](data:image/png;base64,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)
tan
= ![r over h](data:image/png;base64,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)
![tan 30 degree space equals space r over h
tan 30 degree space equals space fraction numerator 1 over denominator square root of 3 end fraction
r space equals space fraction numerator h over denominator square root of 3 end fraction](data:image/png;base64,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)
Volume of conical vessel (V) = ![1 third πr squared straight h](data:image/png;base64,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)
V = ![1 third straight pi straight h squared over 3 straight h space equals space 1 over 9 πh cubed](data:image/png;base64,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)
Differentiating the above wrt to time
![fraction numerator d v over denominator d t end fraction space equals space 1 over 9 straight pi straight d over dt left parenthesis straight h cubed right parenthesis
straight d over dt open parentheses straight x to the power of straight n close parentheses space equals space straight n space. space straight x to the power of straight n minus 1 end exponent space cross times space dx](data:image/png;base64,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)
![fraction numerator d v over denominator d t end fraction space equals space straight pi over 9 cross times 3 h squared space cross times fraction numerator d h over denominator d t end fraction
S u b s t i t u t i n g space t h e space v a l u e s space o f space h space a n d space fraction numerator d h over denominator d t end fraction
fraction numerator d v over denominator d t end fraction space equals space space straight pi over 9 cross times space 3 space cross times left parenthesis 6 right parenthesis squared cross times 1
fraction numerator d v over denominator d t end fraction space equals space 12 straight pi](data:image/png;base64,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)
Thus, the rate at which the volume of water in the vessel is decreasing when its height is 6ft. is ![12 straight pi](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAANCAYAAADISGwcAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAMtJREFUeNpjYEAFakBcC8QXGLADayBeA8SfgPgXVF00AxXBYiBOA+L/OOQPAnEkEPNA+VpAfBQqRlXwnwS18kB8aSAdAAI/0PiC0Oj5AzULF6aKAyyh0YAMjIG4FYhZsJj1g5ohwAHEJ6GJk1izqOYAUDBvAGI3Es2iigOUoJarkGHWH0odoAHEs4GYi8ho+kNO9OJSJA7Eq6CJixjAhCXIvwExG7kO2AINAVLKiC9oYsehpa0WLovx5VVS83QWEO9AE/OChkIXw2AAAL6LQgGfyWChAAAAb3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbj4xMjwvbW4+PG1pIG1hdGh2YXJpYW50PSJub3JtYWwiPiYjeDNDMDs8L21pPjwvbWF0aD4aCQgtAAAAAElFTkSuQmCC)
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