A hotel maintenance team is installing a new cylindrical hot water heater. The interior of… — Armed Services Vocational Aptitude Battery (ASVAB)

A hotel maintenance team is installing a new cylindrical hot water heater. The interior of the heater has a diameter of $4\text{ feet}$ and a height of $7\text{ feet}$ . Using $\frac{22}{7}$ for $\pi$ , how many minutes will it take to completely fill the empty heater if water flows in at a constant rate of $4\text{ cubic feet}$ per minute?

Cevap: 22 minutes

Cevap

It will take 22 minutes to completely fill the hot water heater.

The correct answer is found by first calculating the volume of the cylindrical heater using the formula

V = \pi r^2 h

. Given the diameter of

4\text{ feet}

, the radius is

2\text{ feet}

. Substituting the given values:

V = \frac{22}{7} \times 2^2 \times 7 = 88\text{ cubic feet}

. Dividing this total volume by the fill rate of

4\text{ cubic feet}

per minute gives the total time:

88 \div 4 = 22\text{ minutes}

Adım Adım Çözüm

Determine the radius of the cylindrical heater.

Radius =

2\text{ feet}

The volume formula requires the radius, which is half of the given diameter (

4\text{ feet}

Calculate the total volume of the cylinder.

Volume =

88\text{ cubic feet}

Using the formula

V = \pi r^2 h

with

r = 2

h = 7

, and

\pi = \frac{22}{7}

, we get

V = \frac{22}{7} \times 2^2 \times 7 = 88

Calculate the time required to fill the heater.

Time =

22\text{ minutes}

Dividing the total volume (

88\text{ cubic feet}

) by the flow rate (

4\text{ cubic feet}

per minute) gives the required time.

Anahtar Kavram

Cylindrical Volume Applications

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