Question

The number of houses that can be served by a water pipe varies directly as the square of the diameter of the pipe. A water pipe that has a​ 10-centimeter diameter can supply 40 houses. a. How many houses can be served by a water pipe that has a 30​-centimeter ​diameter? b. What size of water pipe is needed for a new subdivision of 1440 ​houses?

Answer 1

Answer:

Step-by-step explanation:

Given

no of houses that can be served by water is directly Proportional to the square of diameter

$N\propto d^2$

$N=kd^2$

where k =constant

10 cm diameter can supply 40 houses

$40=k(10)^2$-----------1

For d=30 cm Pipe

$N_1=k(30)^2$-------------2

divide 1 & 2

$\frac{N_1}{40}=(\frac{30}{10})^2$

$N_1=40\times 9=360$

(b)for N=1440 houses

$1440=k(d_2)^2$ ----------------3

$\frac{1440}{40}=(\frac{d_2}{10})^2$

$d_2=6\times 10$

$d_2=60 cm$