Math Problem Statement

If the water is dripping out from a conical vessel of semi- vertical angle π/4 at a uniform rate of 2 cm³/s through a tiny hole at the vertex in the bottom. When the slant height of the water is 4 cm, find the rate of-

(a) decrease of the water level.

(b) decrease of the slant height.

(c) decrease of the water surface area.

(d) decrease of the wetted surface of the vessel.

Solution

To solve this problem, let's break it down step by step.

Given:

  • The semi-vertical angle of the cone, θ=π4\theta = \frac{\pi}{4}.
  • The rate of change of volume, (\frac{dV}{dt} = -

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Calculus

Formulas

Volume of a cone
Related rates in calculus

Theorems

-

Suitable Grade Level

Advanced High School

Related Recommendation

Calculating the Pumping Rate into a Leaking Inverted Conical Tank Using Related Rates

Related Rates Problem: Water Dripping from a Conical Funnel with a 120 Degree Vertical Angle

Related Rates Problem: Water Level in Conical Container

Related Rates Problem: Volume Change in Inverted Cone Reservoir

Related Rates Problem: Water Tank with Leaking and Pumping Rates