Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 54

A tank is in the shape of an inverted cone, having height \(h=2.5 \mathrm{~m}\) and base radius \(r=0.75 \mathrm{~m} .\) If water is poured into the tank at a rate of \(15 \mathrm{~L} / \mathrm{s}\), how long will it take to fill the tank?

Short Answer

Expert verified
Answer: The tank will take approximately 117.87 seconds to fill at a rate of 15 L/s.

Step by step solution

01

Find the volume of the cone

To find the volume (V) of the cone, we will use the formula: \(V = \dfrac{1}{3} \pi r^2 h\) Where \(r\) is the base radius, and \(h\) is the height of the cone.
02

Substitute values and calculate the tank volume

Given \(r = 0.75 \mathrm{~m}\) and \(h = 2.5 \mathrm{~m}\), substitute the values into the volume formula: \(V = \dfrac{1}{3} \pi (0.75)^2 (2.5)\) Now, calculate the volume: \(V ≈ 1.768 \mathrm{~m^3}\)
03

Convert the volume to liters

1 cubic meter (\(\mathrm{m^3}\)) is equal to 1000 liters. So to convert \(1.768 \mathrm{~m^3}\) to liters, multiply by 1000: \(1.768 \times 1000 ≈ 1768 \mathrm{~L}\)
04

Find the time to fill the tank

Given the rate of water being poured is \(15 \mathrm{~L/s}\), we can find the time (t) it takes to fill the tank by dividing the total volume by the rate: \(t = \dfrac{\text{total volume}}{\text{rate}}\) Substitute the values and calculate the time: \(t = \dfrac{1768}{15} ≈ 117.87 \mathrm{~s}\)
05

Interpret the result

The tank will take approximately \(117.87\) seconds to fill at a rate of \(15 \mathrm{~L/s}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Express the vectors \(A=\left(A_{x}, A_{y}\right)=(-30.0 \mathrm{~m},-50.0 \mathrm{~m})\) and \(\vec{B}=\left(B_{x}, B_{y}\right)=(30.0 \mathrm{~m}, 50.0 \mathrm{~m})\) by giving their magnitude and direction as measured from the positive \(x\) -axis.

If \(\vec{A}\) and \(\vec{B}\) are vectors and \(\vec{B}=-\vec{A},\) which of the following is true? a) The magnitude of \(\vec{B}\) is equal to the negative of the magnitude of \(\vec{A}\). b) \(\vec{A}\) and \(\vec{B}\) are perpendicular. c) The direction angle of \(\vec{B}\) is equal to the direction angle of \(\vec{A}\) plus \(180^{\circ}\) d) \(\vec{A}+\vec{B}=2 \vec{A}\).

The resultant of the two-dimensional vectors \((1.5 \mathrm{~m}, 0.7 \mathrm{~m})\), \((-3.2 \mathrm{~m}, 1.7 \mathrm{~m}),\) and \((1.2 \mathrm{~m},-3.3 \mathrm{~m})\) lies in quadrant _________. a) I b) II c) III d) IV

Find the vector \(\vec{C}\) that satisfies the equation \(3 \hat{x}+6 \hat{y}\) \(10 \hat{z}+\vec{C}=-7 \hat{x}+14 \hat{y}\)

If you draw a vector on a sheet of paper, how many components are required to describe it? How many components does a vector in real space have? How many components would a vector have in a four-dimensional world?
See all solutions

Recommended explanations on Physics Textbooks

Circular Motion and Gravitation

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Astrophysics

Read Explanation

Kinematics Physics

Read Explanation

Radiation

Read Explanation

Conservation of Energy and Momentum

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free