Respuesta :
Answer:
Therefore the volume of the can is 1256.625 inches cubes.
Step-by-step explanation:
The volume of can directly proportional to the height of the can and the square of the radius.
[tex]V\propto hr^2[/tex]
V= The volume of the can
h= Height of the can
r= radius of the can.
[tex]\therefore \frac{V_1}{V_2}=\frac{h_1r_1^2}{h_2r_2^2}[/tex]
Here [tex]V_1=[/tex] 402.12 inches cubes, [tex]h_1=[/tex] 8 inch, [tex]r_1=[/tex] 4 inch, [tex]h_2=[/tex] 10 inch, [tex]r_2=[/tex] 2 inch, [tex]V_2=?[/tex]
[tex]\therefore \frac{V_1}{V_2}=\frac{h_1r_1^2}{h_2r_2^2}[/tex]
[tex]\Rightarrow \frac{402.12}{V_2}=\frac{8\times 4^2}{10\times 2^2}[/tex]
[tex]\Rightarrow \frac{V_2}{402.12}=\frac{10\times 2^2}{8\times 4^2}[/tex]
[tex]\Rightarrow {V_2}=\frac{10\times 2^2}{8\times 4^2}\times {402.12}[/tex]
[tex]\Rightarrow V_2=1256.625[/tex] inches cubes
Therefore the volume of the can that has 2 inch radius and 10 inch height is 1256.625 inches cubes.
