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Joy has designed a rainwater collection system to store rainwater for her gardening needs. Using a large conical storage tank and gutters to direct water into the tank, she can collect enough water for her yearly gardening needs.

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Joy has designed a rainwater collection system to store rainwater for her gardening needs. Using a large conical storage tank and gutters to direct water into the tank, she can collect enough water for her yearly gardening needs. At the start of a rainstorm, she notices her tank has 16  inches of water in it. The rainstorm lasts for 40 minutes.

  • Let h(t) be the height (in inches) of the water in the tank t minutes after the start of the rainstorm. Assume h(t) defines an invertible function.

 

  • Let V(h) be the volume (in gallons) of water in the tank when the water is at height h (in inches). Assume V(h) defines an invertible function.

 

  • Let r(t) be the rate (in gallons per minute) at which the volume of water in the tank is increasing t minutes after the storm starts. Assume that r(t)>0 for the entire duration of the rainstorm.

 

Which of the following numbers represents the depth, in inches, of water in the tank when the tank contains  60 gallons of water?

 
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