Respuesta :
the new radius be to meet the client's need is 4.9 cm .
Step-by-step explanation:
Here we have , can company makes a cylindrical can that has a radius of 6 cm and a height of 10 cm. One of the company's clients needs a cylindrical can that has the same volume but is 15 cm tall. We need to find What must the new radius be to meet the client's need . Let's find out:
Let we have two cylinders of volume [tex]V_1 , V_2[/tex] with parameters as follows :
[tex]r_1=6cm\\h_1=10cm\\r_2=?\\h_2=15cm[/tex]
We know that volume of cylinder is [tex]\pi r^2h[/tex] , According to question volume of both cylinder is equal i.e
⇒ [tex]V_1=V_2[/tex]
⇒ [tex]\pi (r_1)^2h_1= \pi (r_2)^2h_2[/tex]
⇒ [tex](r_1)^2h_1= (r_2)^2h_2[/tex]
⇒ [tex]\frac{(r_1)^2h_1}{h_2}= (r_2)^2[/tex]
⇒ [tex](r_2) =\sqrt{ \frac{(r_1)^2h_1}{h_2}}[/tex] Putting all values
⇒ [tex](r_2) =\sqrt{ \frac{(6)^2(10)}{15}}[/tex]
⇒ [tex](r_2) =\sqrt{ \frac{36(10)}{15}}[/tex]
⇒ [tex](r_2) =\sqrt{ \frac{360}{15}}[/tex]
⇒ [tex](r_2) =\sqrt{24}[/tex]
⇒ [tex](r_2) =4.9cm[/tex]
Therefore , the new radius be to meet the client's need is 4.9 cm .
