Question

The volume of a can varies jointly as the height of the can and the square of the radius. A can with an 8 inch height and 4 inch radius has a volume of 402.12 inches cubed. What is the volume of a can that has a 2 inch radius and a 10 inch height

Answer 1

Therefore the volume of the can is 1256.625 inches cubes.

Explanation:

The volume of can directly proportional to the height of the can and the square of the radius.

`V\propto hr^2`

V= The volume of the can

h= Height of the can

r= radius of the can.

`\therefore (V_1)/(V_2)=(h_1r_1^2)/(h_2r_2^2)`

Here
`V_1=` 402.12 inches cubes,
`h_1=` 8 inch,
`r_1=` 4 inch,
`h_2=` 10 inch,
`r_2=` 2 inch,
`V_2=?`

`\therefore (V_1)/(V_2)=(h_1r_1^2)/(h_2r_2^2)`

`\Rightarrow (402.12)/(V_2)=(8* 4^2)/(10* 2^2)`

`\Rightarrow (V_2)/(402.12)=(10* 2^2)/(8* 4^2)`

`\Rightarrow {V_2}=(10* 2^2)/(8* 4^2)* {402.12}`

`\Rightarrow V_2=1256.625` inches cubes

Therefore the volume of the can that has 2 inch radius and 10 inch height is 1256.625 inches cubes.